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Generalizations of Deodhar’s -localization functor

In this paper we generalize the result of Deodhar (see Invent. Math. 57 (1980), 101-118) on a-localization functors. Namely, we show that localization with respect to a larger family of left denominator sets "intertwines" with tensoring by finite-dimensional representations. In the language of the author's previous work, localization with respect to such a left denominator set produces a new example of an a-functor and an a-category.