| This thesis concerns computations of twisted equivariant K-theory functors evaluated on certain spaces. In the second chapter, for simple, compact, simply-connected Lie groups G, I determine Kt+h∨ (LBG) ≅ Rtau LG∧I as an abelian group, where Rtau( LG) is the representation ring of tau-projective, positive energy representations of LG, and -∧I is completion with respect to the augmentation ideal of R (G). In the third chapter, I extend this result, in a way, to general compact Lie groups. Namely, I show that K*( B( LGt∨ )) ≅ R S1⋉LGt ∧I . In the fourth chapter, I compute the twisted equivariant K-theory of G-representation spheres. For adjoint representation spheres Sg , I use the theory of topological buildings developed by Burns and Spatzier. For general representation spheres S✶, I instead use results of Freed, Hopkins, and Teleman. |
