2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61374We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the approximately homogeneous C*-algebras and the class of purely infinite C*-algebras which has been recently classified by Kirchberg and Phillips. This extends the known results for UHF algebras and AF algebras by Powers and Bratteli.33 pages. To be published in Internatinal J. MathOperator Algebras46L30, 46L40text