A generalization of the topological Brauer group

In the present paper we study some homotopy invariants which can be defined by means of bundles whose fiber is a matrix algebra. In particular, we introduce a generalization of the Brauer group in the topological context and show that any of its elements can be represented as a locally trivial bundle With Structure group N(k)(x) k is an element of N. Finally, we discuss its possible applications in the twisted K-theory.