Geodesic
Equivariant Derived Category of Bundles of Projective Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 63-68

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We give an analog of D. O. Orlov's theorem on semiorthogonal decompositions of the derived category of projective bundles for the case of equivariant derived categories. Under the condition that the action of a finite group on the projectivization $X$ of a vector bundle $E$ is compatible with the twisted action of the group on the bundle $E$, we construct a semiorthogonal decomposition of the derived category of equivariant coherent sheaves on $X$ into subcategories equivalent to the derived categories of twisted sheaves on the base scheme. 
@article{TM_2009_264_a6,
     author = {A. Elagin},
     title = {Equivariant {Derived} {Category} of {Bundles} of {Projective} {Spaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {63--68},
     publisher = {mathdoc},
     volume = {264},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_264_a6/}
}
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A. Elagin. Equivariant Derived Category of Bundles of Projective Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 63-68. http://geodesic.mathdoc.fr/item/TM_2009_264_a6/