  Let $k$ be a commutative ring, $H$ a faithfully flat Hopf algebra with
bijective antipode, $A$ a $k$-flat right $H$-comodule algebra. We investigate
when a relative Hopf module is projective over the subring of coinvariants
$B=A^{{\rm co}H}$, and we study the semisimplicity of the category of relative
Hopf modules.
