Equivariant Hopf Galois extensions and Hopf cyclic cohomology

Abstract

We define the notion of equivariant $\times$-Hopf Galois extension and apply it as a functor between the categories of stable anti-Yetter–Drinfeld (SAYD) modules of the $\times$-Hopf algebras involved in the extension. This generalizes the result of Jara–Ştefan and Böhm–Ştefan on associating a SAYD modules to any ordinary Hopf Galois extension.