This question seems to be of interest to a couple of people, so here is an approximate approximation of what I was doing.
First of all, the reason why no new matches were shown at all was because I did not call [GKTurnBasedMatch loadMatchesWithCompletionHandler:]every time I wanted the performance to be updated as if I were. So, I do not remember that there is no real problem.
, GKTurnBasedMatch, (.. ) . , [GKTurnBasedMatch loadMatchesWithCompletionHandler:], , GKTurnBasedMatch. , , [match loadMatchDataWithCompletionHandler:], , [GKTurnBasedMatch loadMatchesWithCompletionHandler:] ( match GKTurnBasedMatches). , , NSData. NSData, , , .
, loadMatchDataWithCompletionHandler GKTurnBasedMatch, , .