A Dixmier-Douady theory for strongly self-absorbing C*-algebras II: the Brauer group

We have previously shown that the isomorphism classes of orientable locally trivial fields of C*-algebras over a compact metrizable space X with fiber D circle times K, where D is a strongly self-absorbing C*-algebra, forman abelian group under the operation of tensor product. Moreover this group is isomorphic to the first group (E) over bar (1)(D)(X) of the (reduced) generalized cohomology theory associated to the unit spectrum of topological K-theory with coefficients in D. Here we show that all the torsion elements of the group (E) over bar (1)(D)(X) arise from locally trivial fields with fiber D circle times M-n (C), n >= 1, for all known examples of strongly self-absorbing C*-algebras D. Moreover the Brauer group generated by locally trivial fields with fiber D circle times M-n (C), n >= 1 is isomorphic to Tor((E) over bar (1)(D)(X)).