  A general Mackey type decomposition for representations of semisimple Hopf
algebras is investigated. We show that such a decomposition occurs in the case
that the module is induced from an arbitrary Hopf subalgebra and it is
restricted back to a group subalgebra. Some other examples when such a
decomposition occurs are also constructed. They arise from gradings on the
category of corepresentations of a semisimple Hopf algebra and provide new
examples of Green functors in the literature.
