Actually, Alexander the Great was very probably Greek, in that the King of the Macedonians was entitled to take part in the Olympic Games, which were open to Greeks only. The status of his subjects is rather more doubtful; I suppose it's rather like whether we consider the Cornish to be 'English' or something of their own. That said, his empire can barely be considered Greek in the form that Pericles or even Epaminondas would have recognised; by the time the rather un-Greek idea of monarchy and other generally foreign Macedonian influences had mingled with Alexander's rather bizzare fetish for Persian and other Eastern cultures with a small influence from 'real' Greece his empire was a completely different beast altogether. The nearest thing we have to a 'Greek Empire' is Athens' Delian League, and the status of that as an empire is rather doubtful; it depends on whether a republic can be said to lead an empire (although the French Empire is a commonly used phrase) and whether Athenian control over its 'allies' amounted to actual dominance in effect.