Separable functors for the category of Doi-Hopf modules, applications

We prove a Maschke type theorem for the category of Doi-Hopf modules. In fa ct, we give necessary and sufficient conditions for the functor that forget s the C-coaction to be separable. This leads to a generalized notion of int egrals. Our results can be applied to obtain Maschke type theorems For Yett er-Drinfel'd modules, Long dimodules, and modules graded by G-sets. Existin g Maschke type theorems due to Doi and the authors are recovered as special cases. (C) 1999 Academic Press.