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Given a smooth variety $Y$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}[Y/G]$, of $G$-equivariant coherent sheaves on $Y$ into subcategories equivalent to derived categories of smooth varieties, we construct a similar semiorthogonal decomposition for a smooth $G$-invariant divisor in $Y$ (under certain technical assumptions). Combining this procedure with the semiorthogonal decompositions constructed in [PV15], we construct semiorthogonal decompositions of some equivariant derived categories of smooth projective hypersurfaces.

Semiorthogonal decompositions of equivariant derived categories of invariant divisors