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 $A\# H\otimes_{A}(A \#H \#H^{*})\otimes_{A\# H}M$?,