  We present a precise definition of extended homotopy quantum field theories
and develop an orbifold construction for these theories when the target space
is the classifying space of a finite group $G$, i.e. for $G$-equivariant
topological field theories. More precisely, we use a bicategorical version of
the parallel section functor to associate to an extended equivariant
topological field theory an ordinary extended topological field theory.
Thereby, we give a unification, geometric underpinning and vast generalization
of algebraic concepts of orbifoldization. In the special case of
3-2-1-dimensional equivariant topological field theories, we investigate the
equivariant modular structure on the categories that such theories yield upon
evaluation on the circle. By means of our orbifold construction this
equivariant modular structure will be related to the modular structure on the
orbifold category. We also generalize our orbifold construction to a
pushforward operation along an arbitrary morphism of finite groups and hence
provide a valuable tool for the construction of extended homotopy quantum field
theories.
