Let H be a finite dimensional quasi-Hopf algebra over a field k and A a right H-comodule algebra in the sense of Hausser and Nill. We first show that on the k-vector space A H^* we can define an algebra structure, denoted by A H^*, in the monoidal category of left H
Nearby in the stack
-modules (i.e.
A H^*
is an
H
-module algebra. Then we will prove that the category of two-sided
(A,H)
-bimodules
is isomorphic to the category of relative
( A H^*, H^*)
-Hopf modules, as introduced in by Hausser and Nill. In the particular case where
A=H
, we will obtain a result announced by Nill. We will also introduce the categories of Doi-Hopf modules and two-sided two-cosided Hopf modules and we will show that they are in certain situations isomorphic to module categories.