To display the Game Center screen, initialize a new GKGameCenterViewController object and set its delegate. Optionally, you can choose to configure the view controller further to specify which content is initially displayed. Then present the view controller. Your delegate is called when the user dismisses the screen. Listing 1 shows how to present a new GKGameCenterViewController and display the scores for a specific leaderboard.
Your game should pause other activities before presenting the Game Center user interface.
Configuring the Game Center View Controller’s Delegate