Twisted orbifold K-theory (Q1416888)

The authors define and study the orbifold \(K\)-theory \(K^*_{orb} (X)\) of an orbifold \(X\). They do this by using equivariant methods. In particular, by using techniques from equivariant \(K\)-theory, they construct a Chern character and describe a multiplicative decomposition for \(K^*_{orb}(X) \otimes\mathbb{Q}\), showing that it is additively isomorphic to the orbifold cohomology of \(X\). Moreover, the authors use the theory of projective representations to define the notion of twisted orbifold \(K\)-theory in the presence of discrete torsion, and they obtain an explicit expression for this in some cases.