The message property of GKTurnBasedMatch allows changing the text in the push notification that the next participant receives, but how can I localize it? I tried using Localizable.strings but that doesn't work. I know that regular push notification can easily be localized, but since Game Center has full control over these notifications it seems impossible to do this.
I struggled with the same problem a few months back.
I ended creating a user class with information about which localization the user was preferring, and then let the other player decide language.
something like:
Not really elegant but working.