Gemara

(Mishnah): If an Oni takes an object from the Ba'al ha'Bayis' hand (inside) and takes it outside, he is liable, and the Ba'al ha'Bayis is exempt.

3a: The Ba'al ha'Bayis is exempt, and he is permitted.

17b (Mishnah - Beis Shamai): One may not sell to a Nochri, or help him load a donkey or himself, unless he can reach his destination before Shabbos;

Beis Hillel permit until the sun [sets].

19a (Beraisa): One may put food in front of a Nochri in the Chatzer. If he takes it out, we are not concerned.

Pesachim 6a (Beraisa): If a Nochri deposited Chametz with a Yisrael [with Acharayos, i.e. liability to pay if it is lost or stolen], the Yisrael must destroy it;

If he fixed a place for it, he need not destroy it, for it says "Lo Yimatzei"

Question: What does this mean? (The verse forbids!)

Answer #1 (Rav Papa): The verse teaches about the Reisha. If he deposited it with him, he must destroy it, for it says "Lo Yimatzei."

Answer #2 (Rav Ashi): The verse teaches about the Seifa. If he fixed a place for it, he need not destroy it, for it says "Lo Yimatzei b'Vateichem." It is not consider the Yisrael's house. The Nochri takes into his own Reshus.

Inference: A renter acquires.

Question (Mishnah): One may not rent a house to Nochrim for residence, for the Nochri would bring in his idolatry. (The Yisrael would transgress "v'Lo Savi So'evah El Beisecha").

Answer: Here is different, for it says "Lo Yimatzei" - it is forbidden only if one is Matzuy (frequent) in the place [of the Chametz]. Since it is designated for the Nochri, the Yisrael is not frequent there.

Rishonim

Rambam (Hilchos Shabbos 6:19): On Erev Shabbos one may not sell items to a Nochri, or lend to him or give to him a security or gift, unless he will remove it from the Yisrael's house before Shabbos. While he is in the house, people do not know when he gave to him, and when the Nochri leaves on Shabbos, it looks like he lent to the Nochri or gave a security or stipulated with him or sold to him on Shabbos.

Rosh (1:1): The Gemara says that when the Oni stuck his hand in the house and took from the Ba'al ha'Bayis' hand, the Ba'al ha'Bayis is exempt and totally permitted. Why is this? He transgresses "v'Lifnei Iver Lo Siten Michshol"!

Suggestion: Perhaps we discuss a Nochri. The Gemara said 'the Oni is liable' just for a Siman that if he would be a Yisrael, he would be liable.

Rejection: In any case, there is an Isur mid'Rabanan like it says on 19a. One may put food in front of a Nochri in the Chatzer. If he takes it out, we are not concerned. This implies that this is only when he is in the Chatzer, but if he was outside and stuck his hand in, it is forbidden, for it looks like he gives to him in order that he take it out.

Answer #1: Here we discuss when it is the Nochri's item. Then we do not forbid lest it look like he gives to him in order to take it out, since it does not belong to the Ba'al ha'Bayis.

Rebuttal (Rosh): In Ashkenaz, some forbid even with the Nochri's item. This is reasonable. Since it is forbidden because onlookers think that the Yisrael gave to him in order to take it out on Shabbos, we do not distinguish (based on who owns it), for onlookers do not know whose item it is.

Answer #2 (Rosh): Really, I say that we discuss a Yisrael. The Gemara means that there is no Isur Shabbos at all for the Ba'al ha'Bayis, even though it is forbidden due to Lifnei Iver.

Mordechai (253): One may give food to a Nochri in the Chatzer. If he takes it out, we are not concerned. The Riva says that this refers only to food, which he could eat in the Chatzer. Other things, which are normally taken from place to place, even Beis Hillel forbid them. Beis Hillel permit only on Erev Shabbos when he leaves the Yisrael's Reshus during the day. When Shabbos comes, they belong to the Nochri. It is forbidden on Shabbos, for it looks like the Nochri is the Yisrael's agent. R. Yoel derived from the Riva that a Yisrael may not return a security to a Nochri on Shabbos, even if he designated a place for it before Shabbos, for Beis Hillel permit only on Erev Shabbos when he totally leaves the Yisrael's Reshus during the day.

Hagahah: Avi ha'Ezri (his son) permits if he designated a place during the day, for it totally left the Yisrael's Reshus during the day, like it says in Pesachim. One should be stringent.

Tosfos (6a DH Yiched): Rashi explains that the Yisrael did not accept Acharayus. He permitted the Nochri to put it wherever he wants in the house. The Ri disagrees. If so, why does it depend on whether or not he designated a place? Even if he did not, the Gemara concludes that rental acquires! R. Tam says that we discuss even with Acharayus. We learn from "Lo Yimatzei" that it is not considered found, since he designated a place. Rav Papa derives from reasoning that since he designated a place, it is as if he accepted Acharayus for the Nochri's Chametz in the Nochri's house.

Poskim

Shulchan Aruch (OC 246:2): One may not lend any Kli to a Nochri on Erev Shabbos, unless there is time for him to remove it from the Yisrael's house before dark, for an onlooker will think that the Yisrael commanded him to take it out.

Shulchan Aruch (252:1): One may sell to a Nochri on Erev Shabbos and load him up close to dark, as long as he leaves the Yisrael's Reshus during the day.

Beis Yosef (DH Mutar): We hold like Beis Hillel, according to R. Akiva, who says that it suffices for the Nochri to leave the Yisrael's house during the day.

Mishnah Berurah (8): If there is no time for the Nochri to leave during the day, even if the Nochri stipulates to take it on Shabbos, even the sale is forbidden (not only letting him take it out on Shabbos - PF).

Bi'ur Halachah (DH Limkor): The Shulchan Aruch forbids loading the donkey, even if he sold to him beforehand. The same applies to lifting the burden on the Nochri's shoulder.

Bi'ur Halachah (DH mib'Od): If the Nochri left an item with the Yisrael, and came at night to take it, one may be lenient to give to him in pressed circumstances, even if he is not powerful. Since the Isur is only due to Mar'is ha'Ayin, one need not be concerned when it is only suspicion of an Isur mid'Rabanan where people do not see.

Rema: Some permit that the Nochri leaves on Shabbos if the Nochri designated a place in the Yisrael's house during the day. One should be stringent. See (the Rema in) 325:1.

Taz (3): The Mordechai learns from Pesachim 6a. Another proof is from Shabbos 3a. If the Oni took from the Ba'al ha'Bayis' hand, the Ba'al ha'Bayis is exempt and permitted. (I.e. the Oni is a Nochri - Mishbetzos Zahav.) One should be stringent, lest the person (Nochri) get used to doing so. (Levushei Serad - Maharam and) the Mordechai say(s) that Pesachim 6a connotes that even rental acquires only regarding Chametz, due to the verse. This is why the Rema said that one should be stringent. I do not understand Avi ha'Ezri's proofs. There is no proof from Pesachim, for here the concern is Mar'is ha'Ayin, like the Rambam says! If so, designation does not help. We cannot learn from the Ba'al ha'Bayis, for the Rosh says that surely it is forbidden due to Lifnei Iver. The Gemara merely teaches that there is no Isur Shabbos for the Ba'al ha'Bayis. The Rosh wrote that here and in Ashkenaz, some forbid even with the Nochri's item, for onlookers do not know whose item it is. Therefore, one should permit only for a great need or loss. If the Nochri is powerful, surely we permit even without designating a place. Chachamim did not decree in such a case.

Magen Avraham (3): If the Nochri designated a place, it is like his object.

Magen Avraham (4): See what I wrote (242:6). One may be lenient about a loan in a city surrounded by a wall, but one should be stringent about a sale even there, even if the Nochri lives within the wall. When it becomes known that he sold to him, he will say that he sold on Shabbos. People will not say so about a loan, like I wrote (244:5) regarding a field. Especially regarding merchandise such as a linen garment, which is not normally lent, surely it is forbidden. Perhaps one may be lenient if the Nochri is powerful and he designated a place.

Magen Avraham (5): One should be stringent lest the Nochri do so regularly. The Mordechai connotes that it is because the Nochri did not acquire until he removes it (from the house). If so, it is as if he sells it to him on Shabbos. If he designated a place, he truly acquired it. We are not concerned for Hotza'ah, since we hold that the Ba'al ha'Bayis is exempt and permitted. He says that many disagree, and it is acquired only for Chametz. See what I wrote (246:8). We hold like this. Also regarding Chametz, we hold (440:1) that designating a place does not help, and also in Siman 347 we forbid. Therefore, one may not rely on this to be lenient.

Mishnah Berurah (10): This opinion holds that through designation, it is as if the item is already in the Nochri's house.

Mishnah Berurah (11): Olas Tamid writes that if he rented the room to the Nochri for a Perutah for Shabbos, one need not be stringent at all. The Magen Avraham and other Acharonim are stringent even if he rented it.

Kaf ha'Chayim (14): Eliyahu Rabah says that renting is no better than designating.