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Twisted K-Theory with Coefficients in C*-Algebras

Ulrich Pennig,
published 2011-03-25

We introduce a twisted version of K-theory with coefficients in a C*-algebra A, where the twist is given by a new kind of gerbe, which we call Morita bundle gerbe. We use the description of twisted K-theory in the torsion case by bundle gerbe modules as a guideline for our noncommutative generalization. As it turns out, there is an analogue of the Dixmier-Douady class living in a nonabelian cohomology set and we give a description of the latter via stable equivalence classes of our gerbes. We also define the analogue of torsion elements inside this set and extend the description of twisted K-theory in terms of modules over these gerbes. In case A is the infinite Cuntz algebra, this may lead to an interpretation of higher twists for K-theory.

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