  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 and the
local system of Freed-Hopkins-Teleman in their work in twisted K-theory. In the
case in which the orbifold is simply a manifold we recover previous results of
Gawedzki and Brylinski.
