2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76228This paper is a following to math.RT/0410454. For a finite group of Lie type we study the endomorphisms, commuting with the group action, of a Deligne-Lusztig variety associated to a regular element of the Weyl group. We state some general conjectures, in particular that the endomorphism algebra induced on the cohomology is a cyclotomic Hecke algebra, and prove them in some cases. On the way we also prove results on centralizers in braid groups.Representation TheoryAlgebraic Geometry20C33 20F36text