2011/03/21 by Pennig, Ulrich
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1103.4096
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.