  Kasparov defined a distinguished K-homology fundamental class, so called the
Dirac element. We prove a localization formula for the Dirac element in
K-homology of crossed product of C^{*}-algebras. Then we define the
quantization of Hamiltonian G-spaces as a push-forward of the Dirac element.
With this, we develop a K-homological approach to the quantization commutes
with reduction theorem.
