A universal coefficient theorem for twisted K-theory

Abstract: In this paper, we recall the definition of twisted K-theory in various settings. We prove that for a twist $\tau$ corresponding to a three dimensional integral cohomology class of a space X, there exist a "universal coefficient" isomorphism K_{}^{\tau}(X)\cong K_{}(P_{\tau})\otimes_{K_{}(\mathbb{C}P^{\infty})} \hat{K}_{} where $P_\tau$ is the total space of the principal $\mathbb{C}P<sup>{\infty}$-bundle induced over X by $\tau$ and $\hat K_*$ is obtained form the action of $\mathbb{C}P<sup>{\infty}$ on K-theory.