  We 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.
