Non group-theoretical semisimple Hopf algebras from group actions on fusion categories

Understand

Given an action of a finite group G on a fusion category C we give a criterion for the category of G-equivariant objects in C to be group-theoretical, i.e., to be categorically Morita equivalent to a category of group-graded vector spaces.

• We use this criterion to answer affirmatively the question about existence of non group-theoretical semisimple Hopf algebras asked by P.
• Etingof, V.
• Ostrik, and the author in math/0203060.