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An equivariant derived category is **not* an example of a derived category of an abelian category in general, it has a more intricate construction. In the case of the free action it is equivalent to the derived category of the abelian category of equivariant sheaves. I have created just an idea section and wrote down the main references. The apporpriate treatment has been discovered by Valery Lunts and Joseph Bernstein. I just created the entry for the latter. Changes/links/additions/redirects at Alexander Beilinson, equivariant sheaf.
Added to equivariant derived category the qualification that the naive definition is indeed the correct one if the group is discrete.
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