We establish a correspondence between orbifold and singular elliptic genera of a global quotient. While the former is deﬁned in terms of the ﬁxed point set of the action, the latter is deﬁned in terms of the resolution of singularities. As a byproduct, the second quantization formula of Dijkgraaf, Moore, Verlinde and Verlinde is extended to arbitrary Kawamata log-terminal pairs. 1. Introduction One of the fundamental problems suggested by the intersection homology theory is to determine which characteristic numbers can be deﬁned for singular varieties. .