, Volume 245, Issue 3, pp 449-489
Date: 06 Feb 2004

Gerbes over Orbifolds and Twisted K-Theory

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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.

Communicated by A. Connes
The first author was partially supported by the National Science Foundation and Conacyt-México