  We show that the results of the paper Symplectic Reduction and Riemann-Roch
for Circle Actions of Duistermaat, Guillemin, Meinrenken and Wu can be
expressed entirely in K-theory. We show that their quantization is simply a
pushforward in K-theory, and use Lerman's symplectic cutting and the
localization theorem in equivariant K-theory to prove that quantization
commutes with reduction. Only the case where the action is free on the zero
level set of the moment map is addressed.
