Hmm, this is curious...I actually wrote the translation as "He has stopped to play." and it was marked correct, but I see that "Another correct solution" is "He has stopped playing." Does Αυτός έχει σταματήσει να παίζει really mean both? To me, those two phrases in English have quite distinct meanings (indeed, they are almost opposites- "He has stopped to play" means "He has left whatever activity he was doing before and has begun to play" while "He has stopped playing" means "He now no longer plays").

Why is the subjunctive used here and when must it be used?