  Let $\mathcal{G}$ be an algebraic quantum group, $\mathcal{U}$ a compact
quantum subgroup of $\mathcal{G}$ and $A$ a $\mathcal{U}$-comodule algebra. We
consider a $\mathcal{G}$-comodule algebra $A\square_{\mathcal{U}} \mathcal{G}$
and we prove that under some hypothesis $(A\square_{\mathcal{U}}
\mathcal{G})\#\hat{\mathcal{G}}$ is Morita equivalent to
$A\#\hat{\mathcal{U}}$.
