If one stole a hundred dollars in regular cash (e.g. no rare bill editions), and still has those bills, does he have to return those particular bills or can he return any hundred dollars?
It may depend on the condition of the bills when he stole them and when he's repaying the theft. Shulchan Aruch, Choshen Mishpat 360:7 (from Bava Kamma 96b) states:
Needless to say, if the coins are in the same condition as when he stole them, then there has been no change that would make them become his property.
Presumably, then, the same considerations would apply to bills.