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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 $\mathop ⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19032.html} }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 $\mathop ⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.