  We introduce the tracial quasi-Rokhlin property for an automorphism alpha of
a unital C*-algebra A, which is not assumed to be simple. We show that under
suitable hypotheses, the associated crossed product C*-algebra C*(Z,A,alpha) is
simple, and there is a bijection between the space of tracial states on
C*(Z,A,alpha)$ and the alpha-invariant tracial states on A. We show that, for a
minimal dynamical system (X,h) and a simple, separable, unital C*-algebra A,
the automorphism beta which extends the action of h on C(X) has the tracial
quasi-Rokhlin property, and hence that C*(Z,C(X,A),beta) has the structural
properties described above.
