G‐crossed braided zesting.

For a finite group G$G$, a G$G$‐crossed braided fusion category is a G$G$‐graded fusion category with additional structures, namely, a G$G$‐action and a G$G$‐braiding. We develop the notion of G$G$‐crossed braided zesting: an explicit method for constructing new G$G$‐crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects in the category and grading group G$G$. This is achieved by adapting a similar construction for (braided) fusion categories recently described by the authors. All G$G$‐crossed braided zestings of a given category C${\mathcal {C}}$ are G$G$‐extensions of their trivial component and can be interpreted in terms of the homotopy‐based description of Etingof, Nikshych, and Ostrik. In particular, we explicitly describe which G$G$‐extensions correspond to G$G$‐crossed braided zestings. [ABSTRACT FROM AUTHOR]