  The twisted Drinfeld double (or quasi-quantum double) of a finite group with
a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid
is the loop (or inertia) groupoid of the original group and the twisting is
shown geometrically to be the loop transgression of the 3-cocycle. The twisted
representation theory of finite groupoids is developed and used to derive
properties of the Drinfeld double, such as representations being classified by
their characters.
  This is all motivated by gerbes and 3-dimensional topological quantum field
theory. In particular the representation category of the twisted Drinfeld
double is viewed as the `space of sections' associated to a transgressed gerbe
over the loop groupoid.
