  After recalling basic definitions and constructions for a finite group $G$
action on a $k$-linear category we give a concise proof of the following
theorem of Elagin: if $\mathcal{C} = \langle \mathcal{A}, \mathcal{B} \rangle$
is a semiorthogonal decomposition of a triangulated category which is preserved
by the action of $G$, and $\mathcal{C}^G$ is triangulated, then there is a
semiorthogonal decomposition $\mathcal{C}^G = \langle \mathcal{A}^G,
\mathcal{B}^G \rangle$. We also prove that any $G$-action on $\mathcal{C}$ is
weakly equivalent to a strict $G$-action which is the analog of the Coherence
Theorem for monoidal categories.
