Holonomy for gerbes over orbifolds

In this paper we compute explicit formulas for the holonomy map for a gerbe with connection over an orbifold. We show that the holonomy descends to a transgression map in Deligne cohomology. We prove that this recovers both the inner local systems in Ruan’s theory of twisted orbifold cohomology [1] and the local system of Freed–Hopkins–Teleman in their work in twisted K-theory [2]. In the case in which the orbifold is simply a manifold we recover previous results of Gawȩdzki [3] and Brylinski[4].