Gemara

(Beraisa - R. Yosi citing R. Yishmael): Bikurim may be eaten only when the Mikdash stands. We cannot learn Ma'aser from Bikurim, for Bikurim require Hanachah (being placed in front of the Mizbe'ach).

Inference: He did not say that we do not learn from Bikurim, for they require Hanachah and Kri'ah (reciting the Parshah), for he holds that Kri'ah is not Me'akev.

Rejection (Rav Ashi): Even if Kri'ah is not Me'akev, there is a Mitzvah to do Kri'ah. He should have said that we cannot learn from Bikurim because the Mitzvos of Hanachah and Kri'ah apply to them! Rather, he did not ask from Kri'ah because it does not always apply. E.g., a convert does not do Kri'ah, for he cannot say "Asher Nishba Hash-m la'Avoseinu" (that Hash-m swore to our fathers).

Sukah 49b - Question: Why does it say (only) "Nedivei Am Ne'esfu Im Elokei Avraham", and not (also) Elokei Yitzchak v'Yakov?

Answer: Avraham was the beginning of converts.

Bava Basra 81a (Mishnah): If Reuven bought two trees in Shimon's property, he brings Bikurim, but does not recite the declaration (because he cannot say "the land that You, Hash-m, gave to me.")

Rosh Hashanah 29a (Beraisa): Regarding all Berachos, even if one was Yotzei, he can be Motzi.

Berachos 20b - Question (Ravina): Is a woman obligated to say Birkas ha'Mazon mid'Oraisa? If she is, she can exempt men.

Answer (Rava - Beraisa): A tradition from Sinai teaches that a son a slave may bless for his master, and a wife may bless for her husband.

Bikurim (Mishnah 1:4): A convert brings Bikurim but he does not recite, for he cannot say "that You swore to our fathers to give to us." If his mother was a Yisrael, he recites. When he prays alone, he says 'Elokei Avos Yisrael.' When he prays alone in the Beis ha'Keneses, he says 'Elokei Avoseichem.' If his mother was a Yisrael, he says 'Elokei Avoseinu.'

Rishonim

Rambam (Hilchos Bikurim 4:3): A convert brings Bikurim and recites, because Hash-m told Avraham "I made you father of a multitude of nations." Hash-m made him father of the entire world that enters under the wings of the Shechinah. The oath was initially to Avraham that his children wil inherit the land.

Perush ha'Mishnayos (Bikurim 1:4): The Halachah is that a convert recites, unlike the Mishnah. Hash-m made Avraham father of the entire world, since he taught them Emunah and the true creed.Therefore, every convert can say "that Hash-m swore to our fathers."

Rosh (Perush Bikurim 1:4): R. Tam would not let a convert bless Birkas ha'Mazon, for he cannot say "that You bequeathed to our fathers." A Beraisa in Sifri says so, and the Gemara in Makos. The Ri says that he can say 'to our fathers.' The Halachah does not follow this Mishnah. In the Yerushalmi, R. Yehudah says that he can say this, because Hash-m made Avraham the father of all nations. R. Yehoshua ben Levi said that the Halachah follows R. Yehudah. R. Avahu ruled like him in practice. There were no Bikurim in his days. He ruled that when he prays by himself, he says 'Elokei Avoseinu. The Gemara in Makos is like R. Yosi, who cited R. Yishmael. He argues with R. Yehudah. The Halachah follows R. Yehudah, like the Yerushalmi says. Alternatively, the Gemara in Makos is like R. Yehudah. He holds that a convert cannot do Kri'ah because he cannot say 'that You swore to our fathers to give to us', for converts did not receive part of Eretz Yisrael. The Gemara cited only the beginning of the verse, but it relies on the end of it. The Gemara does so in other places. Regarding Keni, i.e. descendants of Yisro, who received a portion of Eretz Yisrael (a fertile patch near Yericho), R. Yehudah taught that a convert recites. R. Tam challenged the Yerushalmi. How can a convert say 'an Arami tried to destroy my father', i.e. Yakov? It seems that it is an errant Beraisa. R. Tam establishes the Tosefta to discuss one whose mother is a Yisraelis. The first Tana says that even such a convert cannot recite (unless he is from Keni), for women received no portion in Eretz Yisrael. It is unlike our Mishnah, which says that if his mother is a Yisraelis, he recites. The Yerushalmi says that a convert's son says 'Elokei Avoseinu'. A Beraisa says so only if his mother is a Yisraelis. It discusses when the father was a Nochri; it is unlike R. Yehudah.

Tosfos (Bava Basra 81a DH Lime'utei): R. Tam challenged the Yerushalmi. How can a convert say "an Arami tried to destroy my father (Yakov) and he descended to Mitzrayim and they did evil to us"? Rather, it is an errant Beraisa. The Ri says that our Mishnah discusses Bnei Keni. It does not help if his mother is from Yisrael. Women do not recite, for women themselves did not receive Eretz Yisrael, even though they inherited it. All the more so her son does not recite (if he is considered a convert), for he is no better than her!

R. Shimshon (Bikurim 1:4): A Tosefta says that the only converts who can recite are Bnei Keni. They can say "that you swore to our fathers", for he (presumably he means that Hash-m authorized Moshe, and Moshe) vowed to Yisro. The Yerushalmi asked why it helps if his mother is from Yisrael. Women did not receive Eretz Yisrael! It does not answer this at all. Perhaps it does not bother to answer, for this is not a question.

Tosfos Yom Tov and Maharsha: It is not a question because even though the land was not promised to his mother, it was promised to his mother's father. The oath was not to those who left Mitzrayim or entered Eretz Yisrael (i.e. those who received portions, from which women were excluded).

Note: It seems that this is unlike Tosfos. It is not clear why this reasoning does not obligate women to recite, for the land was promised to their fathers. All agree that the land was not give it to converts, for Hash-m swore about this to Avram, before he was called Avraham.

Poskim

Shulchan Aruch (OC 53:19): Some do not allow a convert to be a Shali'ach Tzibur. Their words are rejected.

Beis Yosef (DH Kasuv b'Mordechai): The Mordechai (Megilah 786) says that in Wertzberg, they did not allow a convert to be a Shali'ach Tzibur, for he cannot say 'Elokei Avoseinu.' The Mishnah says that he says 'Elokei Avos Yisrael' when he prays alone, and 'Elokei Avoseichem' in the Beis ha'Keneses. R. Yo'el permitted, for the Amora'im (R. Yehoshua ben Levi and R. Avahu) in the Yerushalmi rule like R. Yehudah, who says that he can recite. Tosfos and Hagahos Maimoniyos bring that R. Tam and the Ri argued about this. The Ran (Bava Basra 81a DH veha'Chsiv) rules like the Ri, and says that also the Rambam and Rashba do. It seems that the Rambam agrees.

Eshel Avraham (19): We learned (Rosh Hashanah) that for all Mitzvos (our text says 'Berachos'), even if one was Yotzei, he can be Motzi. I used to think that this excludes women and converts, because Arvus (mutual responsibility) does not apply to them. This is like the Rosh says in Berachos (3:13. Note - the Rosh says so only about women there.) One who was Yotzei can be Motzi due to Arvus. The Shulchan Aruch here proves differently. If we would not say so, how can a convert be Shali'ach Tzibur, and be Motzi people after he was Yotzei?! Even if we will say that Chachamim enacted that he can be Shali'ach Tzibur, how can a Chiyuv mid'Rabanan exempt a Chiyuv mid'Oraisa, according to the Shulchan Aruch, which rules that Tefilah is mid'Oraisa?

Shulchan Aruch (199:4): A convert can bless Birkas ha'Mazon and say 'that You bequeathed to our fathers.'

Beis Yosef (DH u'Mah she'Chosav): R. Tam would not let a convert lead Birkas ha'Mazon. When he blesses for himself, he omits these words. He cannot omit them when being Motzi others, for for them this is changing from the text that Chachamim fixed. If after Birkas ha'Zimun everyone says Birkas ha'Mazon himself, it seems that even R. Tam would agree that a convert can lead. He forbids only when the Mezamen is Motzi the others. I wrote in Siman 53 that the Ramban, Rambam, Rashba, and Ran hold like the Ri. We follow them.