(untitled) (Communications in Mathematical Research, 2021)
We prove a Maschke type theorem for Doi-Hopf π-modules. A sufficient condition for having a Maschke type property is that there exists a suitable total integral map for the Doi-Hopf π-modules in question. The applications of the results are considered. Finally, As an application of the existence of total integral, we prove that ⊕ _α∈π C_α ⊗ A is a generator in the category ^π-C U(H)A.