In the sigma model formalism of string theory twisted K-theory is known to classify the D-brane charges in the presence of a nontrivial flux. The aim of this talk is to explain how to use the machinery of noncommutative geometry to study the twisted K-theory of some infinite dimensional spaces like SU(\infty).We are also going to discuss the dual K-homology theory, which has some physical importance, and construct the corresponding dual Chern-Connes character.