The first half of Acts belongs to Peter. His story climaxes in Acts 10-12, where he presides over the “Gentile Pentecost” that brings Cornelius and his household into the kingdom, is arrested and miraculously released and then departs. He reappears briefly, but for the most part his story in Acts is over. The second half of the book belongs to Paul. Luke wrote a “to the Jew first, and also to the Greeks” account of the early church.
Fittingly, Peter’s finale has to do with the Jew/Gentile issue. He learns from the Cornelius episode that he should call no man unclean, that God shows no partiality, and that God has granted repentance and the Spirit to Gentiles as well as Jews. At the same time, the diaspora of Christian Jews in Antioch begin to preach to Gentiles (11:19-26).
Peter, apostle to the circumcision, ends his story by turning to Gentiles. Just like Paul: Acts 10-12 anticipates the very end of the book, when Paul turns from preaching to the Jews of Rome to preaching to Gentiles.