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The twisted Drinfeld double (or quasi-quantum double) of a finite group witha 3-cocycle is identified with a certain twisted groupoid algebra. The groupoidis the loop (or inertia) groupoid of the original group and the twisting isshown geometrically to be the loop transgression of the 3-cocycle. The twistedrepresentation theory of finite groupoids is developed and used to deriveproperties of the Drinfeld double, such as representations being classified bytheir characters.  This is all motivated by gerbes and 3-dimensional topological quantum fieldtheory. In particular the representation category of the twisted Drinfelddouble is viewed as the `space of sections' associated to a transgressed gerbeover the loop groupoid.Comment: 25 pages, 10 picture

The twisted Drinfeld double of a finite group via gerbes and finite groupoids