H}}$ is the identity pseudofunctor, ${{\mathcal Z}}({\mbox{\rm Id\,}})$ is a braided monoidal category called the *center* of the 2-category.

In Section \[Section:group-2-cat\] we explicitly describe the notion of a group action on a 2-category. Given two 2-categories ${{\mathcal B}},{{\mathcal B}}'$ equipped with an action of a group $G$, we define the notion of $G$-pseudofunctor between them. When a $G$-pseudofunctor is a biequivalence, we say that ${{\mathcal B}},{{\mathcal B}}'$ are $G$-biequivalent. Also, we define the notions of $G$-pseudonatural transformation and $G$-modifications. All these data, turns out to be a 2-category, denoted by ${\textbf{2Cat}}^G({{\mathcal B}},{{\mathcal B}}')$. The equivariant 2-category is ${{\mathcal B}}^G={\textbf{2Cat}}^G(\mathcal{I},{{\mathcal B}})$, where $\mathcal{I}$ is the unit 2-category, where $G$ acts trivially.

In Section \[Section:coherence\] we prove that any 2-category with a group action is $G$-biequivalent to another one where the action is *strict*. Section \[Section:equivariant\] is devoted to explicitly describe all ingredients in the equivariant 2-category ${{\mathcal B}}^G$.

In Section \[Section:examples-from-cat\] we show an example coming from graded tensor categories. If ${{\mathcal D}}=\oplus_{g\in G} {{\mathcal D}}_g$ is a $G$-graded tensor category, then the group $G$ acts on the 2-category ${}_{{{\mathcal D}}_1}{\mbox{\rm Mod\,}}$ of left ${{\mathcal D}}_1$-modules. The resulting equivariant 2-category $({}_{{{\mathcal D}}_1}{\mbox{\rm Mod\,}})^G$ is biequivalent to ${}_{{{\mathcal D}}}{\mbox{\rm Mod\,}}$. In 