Modular GG-graded algebras and GG-algebras of endomorphisms

We study Clifford Theory and field extensions for strongly group-graded algebras. In [Turull, A., Clifford theory and endoisomorphisms, J. Algebra 371 (2012), 510–520] and [Turull, A., Endoisomorphisms yield mo-dule and character correspondences, J. Algebra 394 (2013), 7–50] the author introduced the notion of endoisomorphism showing that there is a natural connection between it and Clifford Theory of finite group algebras. An endoisomorphism is an isomorphism between GG-algebras of endomorphisms, where GG is a finite group. We consider here endoisomorphisms between modules over strongly GG-graded algebras. An endoisomorphism induces equivalences of categories with some good compatibility properties.