For a finite-dimensional semisimple-cosemisimple Hopfalgebra $H$, a finite-dimensional twisted $H$-module algebra $A$ and a cocycle $\sigma\in \Hom_{k}(H \otimes H, A)$. Suppose that $A\#_{\sigma} H$ is a crossed product algebra and $M$ is a finitely generated $A \#_{\sigma} H$-module.

Is $M$ a direct summand of $(A \#_{\sigma} H)\otimes_{A}(A \#_{\sigma}H\#H^{*}) \otimes_{A \#_{\sigma}} X$?