Who are the people of God? Luke's purposes in Acts are to identify the Church, to establish the legitimacy of its gospel and to demonstrate that God was an active force in history. He shows that the communities of Jewish and Gentile Christians are the true heirs of God's promises to Israel. This is a theological interpretation of the history of the Church within history: Luke is an artist, a narrator rather than a systematic theologian, but he writes about the roles of God, Christ and the Holy Spirit and of the Church.
If you are a serious student of Acts, you must read Jervell (though his earlier translated works may be clearer). Jervell's primary insight is to set the book of Acts within the milieu of the Diaspora synagogue.
Over and against the view that Acts is the story of Gentile Christianity, Jacob Jervell shows that the Church is the remnant of true Israel. This book challenges all assumptions on why Luke wrote Acts. It is a must read for students of the New Testament.
I wanted to like this volume more than I did. Overall, it is scholarly and well-written with a logical argument. This is, I think, the book's weakness -- the argument (that the church discussed in Acts is almost 100% Jewish / God-fearer in make-up and that there are no Gentile believers in the early Church) is fairly unfounded.
A sub-argument, which has some merit however, is that the purpose of the Church was to redemptively restore the nation of Israel back to its place as the missional agent of God's plan in the world. Overall, the exegesis is solid. However, his interpretations travel down a path that leads to a lot of head-scratching.