On tensor categories attached to cells in affine Weyl groups, III
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We prove a weak version of Lusztig's conjecture on explicit description of the asymptotic Hecke algebras (both finite and affine), and explain its relation to Lusztig's classification of character sheaves.
19 pages, mistake in Section 5.4 is corrected, other minor corrections; Appendix added
19 pages, mistake in Section 5.4 is corrected, other minor corrections; Appendix added