2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62394We prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algebras some 30 years ago.This generalizes and replaces the paper(math.OA/0104258) with a similar title by A. Kishimoto and S. SakaiOperator Algebras46L30, 46L40text