GKLocalPlayer *localPlayer = [GKLocalPlayer localPlayer];

 localPlayer.authenticateHandler = ^(UIViewController *loginVC, NSError *error) {
    if ([GKLocalPlayer localPlayer].authenticated) {
        // authentication successful
    }
    else if (loginVC) {
        // player not logged in yet, present the vc
        [self presentViewController:loginVC animated:YES completion:nil];
    }
    else {
        // authentication failed
    }
};

GKScore *score = [[GKScore alloc] init];
if (score) {
    score.value = self->selectedScore;
    NSArray* scoreArray = [[NSArray alloc]initWithObjects:score, nil];
    //score.category = @"High Scores";

    UIActivityViewController *avc = [[UIActivityViewController alloc]
                                     initWithActivityItems:scoreArray applicationActivities:nil];
    avc.completionHandler = ^(NSString *activityType, BOOL completed) {
        if (completed)
            [self dismissViewControllerAnimated:YES completion:nil];
    };

    if (avc)
        [self presentViewController:avc animated:YES completion:nil];
}