Abstract :
We prove a Maschke type theorem for Doi–Hopf modules. A sufficient condition in order to have a Maschke type property is that there exists a normalized integral map for the Doi–Hopf datum in question. The results are applied to graded modules and to Yetter–Drinfelʹd modules. As another application, a characterization of cosemisimple coalgebras over a field is given.
