"Who am I? Who are you?"
The Doppleganger usually has the same abilities, obsessions and skills of the mage that created it...but these can vary wildly.
Dopplegangers are created when a mage doubles back in time. The "real" version of himself and the "possible" version of himself conflict and split apart into two distinct beings -- the real Sam the Mage and the alternate-reality Sam the Mage (unless you're *really* twisted, assume that the current timeline is the real one and the PC is the real Sam the Mage. Because if not, then the real mage is actually the imposter. Of course...this would be a very mean thing to do and you should never, EVER pull this one on your players. EVER).
To try and clarify this, imagine you're Sam the Mage, Chronomancer. One day when you were nineteen, some guy offered you fifty bucks to carry a package across town and deliver it to some address you never heard of. You decline.
Now you use the Anachron spell to return to that age. To the current timeline, that encounter happened and you declined the offer and you went on with your life. But now, to you in your nineteen year old body, it hasn't happened. Or maybe it did and you declined again. or maybe you accepted the offer and then went on to do more jobs for this guy, until you learned he was in the Syndicate, until you joined the mob, until you...and so on. Now you find out that the Mafia don that someone hired you to take out is actually *you*. Well, you as you might have been...
Dopplegangers are notoriously foul-tempered about these temporal screw-ups, especially because you've plucked them out of a life that they knew into one that's fairly alien to them. Suddenly the Mafia don looks different...his men are confused. The Mafia don is confused...this isn't his life, it's yours.