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 $\mathbb{C}P^{\infty}$-bundle induced over
X by $\tau$ and $\hat K_*$ is obtained form the action of
$\mathbb{C}P^{\infty}$ on K-theory.