Gemara

(Mishnah): If one sold his field to Nochrim, for Tikun ha'Olam he buys the fruit to bring (to the Mikdash) Bikurim (the first Peros to ripen of the seven species).

(Rabah): Ein Kinyan l'Nochri b'Eretz Yisrael (a Nochri cannot acquire land in Eretz Yisrael to exempt what grows from Ma'aser). "To Me (Hash-m) is the land" - the Kedushah of the land is (always) Mine.

(R. Elazar): Yesh Kinyan l'Nochri b'Eretz Yisrael - "(you will tithe) your grain", not the grain of Nochrim.

R. Elazar expounds "your Degen (grain)", not grain of Nochrim. Rabah expounds "your Digun (Miru'ach, final processing of grain)", not the Digun of Nochrim.

Support (for R. Elazar - R. Chiya bar Aba): The Mishnah obligates bringing Bikurim from a field sold to Nochrim for Tikun ha'Olam. Mid'Oraisa, it is exempt!

Rejection (Rav Ashi): Really, Ein Kinyan. At first, one who sold brought Bikurim mid'Oraisa. People sold, for they felt that the land retains its Kedushah. It was enacted not to bring Bikurim. Chachamim saw that (to be exempt from Bikurim), people left the field with the Nochri, so they enacted that people bring again.

Bava Metzia 101a (Mishnah - R. Yehudah): A sharecropper on his ancestors' field that (now) belongs to a Nochri must tithe even the half that the Nochri gets.

'His ancestors' field' refers to Eretz Yisrael, which belonged to the Avos. R. Yehudah holds that Ein Kinyan l'Nochri, and that a sharecropper is like a Choker (a renter who pays a fixed amount of Peros each year); who must tithe and pay the Nochri whether or not the field produces, for he pays a debt.

Question (Rav Kahana - Beraisa - R. Yehudah): A sharecropper on his ancestors' field now owned by a Nochri extortionist must tithe even the Nochri's share.

Why does the Beraisa discuss an extortionist? This applies to any Nochri!

Answer: Rather, R. Yehudah holds that Yesh Kinyan, and a sharecropper is not like a Choker. The field belonged to his father or grandfather. We fine the original owners' heirs to tithe. Since the field is dear to them, they will work it anyway.

(R. Yochanan): The fine encourages the heir to buy it back from the Nochri.

Avodah Zarah 20b (Mishnah - R. Meir): In Surya, we may not rent fields to Nochrim;

R. Yosi permits.

They argue about whether or not Kivush Yachid (Surya, which was conquered improperly, and/or not by all of Yisrael) gets Kedushas Eretz Yisrael. We decree to forbid renting, lest one sell, which is forbidden mid'Oraisa.

Bechoros 11a (R. Chanina): If one buys Tevel from a Nochri after Miru'ach, he separates Ma'aseros and keeps them.

Question: Miru'ach Nochri is exempt! We read "Deganecha" like 'Diguncha'.

Answer: The Yisrael did Miru'ach while the produce belonged to the Nochri. He must Ma'aser them, for Ein Kinyan. Even if a Nochri buys land in Eretz Yisrael, it retains its Kedushah, and the produce must be tithed mid'Oraisa;

(R. Yehoshua ben Levi) If one buys Tevel after Miru'ach from a Nochri, he is exempt from giving Terumas Ma'aser.

Rishonim

Rambam (Hilchos Terumos 1:10): If a Nochri bought land in Eretz Yisrael, he did not uproot it from Mitzvos. It keeps its Kedushah. Therefore, if a Yisrael bought it back from him, it is not like Kivush Yachid. Rather, mid'Oraisa he separates Terumah and Ma'aseros and brings Bikurim, as if it was never sold.

Kesef Mishneh: Many Mishnayos in Zera'im connote that Yesh Kinyan, but the Halachah does not follow them. Alternatively, they are when the Yisrael did not buy back from the Nochri. The Rambam discusses when the Yisrael bought back from the Nochri.

Rebuttal (Gra YD 331:8): If the Yisrael did not buy it back, all agree that he need not buy the Peros to tithe them (Rashi 47b DH mid'Oraisa)! If he bought back even the Peros, the Rambam obligates, like the opinion that Ein Kinyan!

Rambam (12): If a Nochri sold attached Peros to a Yisrael before they reached Onas ha'Ma'aseros (enough growth to be liable in Ma'aser), and the Yisrael finished them, they are fully obligated. He gives Terumos and Ma'aseros to those who receive them. If the Yisrael bought after Onas ha'Ma'aseros, he separates tithes and gives according to the calculation. E.g. if it grew a third with the Nochri and finished with the Yisrael, he gives two thirds of the Ma'aser to a Levi and two thirds of the Terumas Ma'aser to a Kohen, and sells the other third to them.

Ba'al ha'Ma'or (Bava Metzia 58a): We concluded that R. Yehudah holds that Yesh Kinyan, or a sharecropper is not like a Choker, and then he could hold Ein Kinyan. Chachamim made a fine so that the Nochri will be unable to find workers, and will sell it back. However, the Beraisa about the extortionist must refer to a field of the Avos. It proves that Yesh Kinyan.

Rebuttal (Ra'avad, Kasuv Sham): It is absurd to fine the Nochri. He helped the Yisrael by buying his field! It is difficult even to fine the Yisrael for the sale of his fathers. Perhaps they had no choice! We cannot discuss a Nochri who stole it, for surely Yesh Kinyan is only when he buys it. Land cannot be stolen! Rather, it is an enactment to encourage the Yisrael to buy it back.

Poskim

Shulchan Aruch (YD 331:3): If a Nochri bought land in Eretz Yisrael, and a Yisrael bought it back from him, he separates Terumah and Ma'aseros.

Beis Yosef (Sof ha'Siman DH u'Mah she'Chosav Rabeinu b'Shem): The Rambam rules like Rabah that Ein Kinyan, because Rav Ashi defended him.

Gra (8): We rule like R. Chanina and R. Yehoshua ben Levi in Bechoros. (Since they exempt Miru'ach of a Nochri, they must hold that Ein Kinyan.) Even though in several places it seems that Yesh Kinyan, we can say that they refer to Surya, or are like R. Meir, who holds that Yesh Kinyan.

Shulchan Aruch (5): If a Nochri sold attached Peros to a Yisrael before Onas ha'Ma'aseros, and the Yisrael finished them, they are totally obligated. He gives all the Ma'aser Rishon to a Levi. If he bought after Onas ha'Ma'aseros, he separates Terumos and Ma'aseros and gives the Ma'aser to a Levi according to the calculation. E.g. if it grew a third with the Nochri, and the rest with the Yisrael, he separates Terumos and Ma'aseros and gives two thirds of the Ma'aser Rishon to a Levi.

Beis Yosef (DH:u'Mah she'Chosav Machar): The first Tana in Ma'aseros 5:5 obligates Peros bought from a Nochri before Onas ha'Ma'aseros, and exempts what Peros bought after this. Rebbi obligates according to how much grew when the Yisrael owned it. The Rambam rules like the first Tana. He holds that this is in Surya, for there Yesh Kinyan, but in Eretz Yisrael all agree that Ein Kinyan. In any case Terumos and Ma'aseros must be separated, because the Yisrael finished them. When he bought after Onas ha'Ma'aseros, he gives for free only the fraction that grew with the Yisrael.