From the research I've done, GameKit seems to be mostly about leaderboards and achievements. I am trying to develop a turn-based game like Words with Friends or Checkers. Can GameKit be used for this? The Game Center app seems to require you and your friend to simultaneously have the app open and invite each other to play. I want the Words With Friends approach where you receive notifications that your friend has made a move. Can GameKit do this?
If not, how is this achieved?