Let $R$ be a commutative ring, $H<G$ a finite group pair. Let $P$ be a $RG$ module that is $RH$ projective. It is known that for any $RG$ module $X$ the tensor $P\otimes X$ is $RH$ projective. This in some sense has to do with Frobenius reciprocity. Is there a similar result for a more general case other than finite dimensional Hopf algebra extensions?