Gerbes over Orbifolds and Twisted K-Theory

Abstract

In this paper we construct an explicit geometric model for the group of gerbes over an orbifold X . We show how from its curvature we can obtain its characteristic class in H 3 ( X ) via Chern-Weil theory. For an arbitrary gerbe , a twisting K orb ( X ) of the orbifold K -theory of X is constructed, and shown to generalize previous twisting by Rosenberg [28], Witten [35], Atiyah-Segal [2] and Bowknegt et. al. [4] in the smooth case and by Adem-Ruan [1] for discrete torsion on an orbifold.