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:
הגוזל מעות ישנות ושיפן וחידשן לא קנה שהרי מתיישנין וחוזרים כשהיו. גזל מעות חדשים וישנן קנה שאם יחדשם פנים חדשות הם
If one steals old coins, and polishes them to make them appear new, he hasn't acquired them [i.e., he needs to return the actual coins], because when they become old again they will look just like they did before [and the halachic principle is that only an irreversible change makes the object become the property of the thief]. But if he stole new coins and aged them, he has acquired them [and need return only their value], because even if he makes them look new again, it is [considered] a new "face" [entity].
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.