  Based on a weak action of a finite group J on a finite group G, we present a
geometric construction of J-equivariant Dijkgraaf-Witten theory as an extended
topological field theory. The construction yields an explicitly accessible
class of equivariant modular tensor categories. For the action of a group J on
a group G, the category is described as the representation category of a
J-ribbon algebra that generalizes the Drinfel'd double of the finite group G.
