In our talk we present a twisted analogue of a result of Hopkins and Hovey who show that the functor which associates to a space $X$ the graded abelian group $\Omega^{spin}_{*}(X) \otimes_{\Omega^{spin}_{*}} KO_{*}(pt)$ yields a geometric description of $KO_{*}(X)$. Our analogue for twisted $K$-theory also gives further inside to a Brown-Douglas approach to twisted $K$-homology. The results are joint work with Baum, Khorami and Schick.