Let be $H$ a finite dimensional semisimple-cosemisimple Hopf algebra, and $A$ be a finite dimensional $H$-module algebra. If $M$ is a finitely generated $A\# H$-module.
Is $M$ a direct summand of $A\# H\otimes_A (A \#H \#H*)\otimes_(A\# H) M$?
A question about the smash product
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