The northern part of cyprus in controlled by the turkish military which invaded the island in 1974 because

Actually, the invasion happened in response to the Coup d'etat: five days before a pro-Greek group performed a coup d'etat on the island with the intention of uniting the Island to Greece. Turkey wanted to protect ethnic Turks (which have lived on the island for generations) on the Island and their invasion was motivated by will to protect ethnic Turks.