Identities of Algebras with Actions of Hopf Algebras

In this publication we consider polynomial identities of algebras admitting an action of a Hopf algebra. If H is a finite-dimensional Hopf algebra over a field F it is interesting to determine the conditions on H which ensure that for any F-algebra A where H acts it follows from the set A^H of H-invariants of A being a Pi-algebra that also A is a PI-algebra. We denote the class of these Hopf algebras 풫.