Abstract
We first prove the fundamental theorem for (weak) relative Hopf group-comodules in this article. Secondly, we introduce the notion of a (weak) group smash product and give a sufficient and necessary condition under which (weak) group smash product algebras and the usual tensor product coalgebra become a (weak) semi-Hopf group-coalgebra. Furthermore, we get a sufficient condition for (weak) group smash product algebras to be semisimple. Finally, we prove an analog of the Blattner–Cohen–Montgomery's duality theorem for (weak) group smash products: For any (weak) π-H-module algebra A, there is a canonical isomorphism between the algebras and End(A # Hα)A.
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