Deformation quantization as the origin of D-brane non-Abelian degrees of freedom

I construct a map from the Grothendieck group of coherent sheaves to Khomology. This results in explicit realizations of K-homology cycles associated with D-brane configurations. Non-Abelian degrees of freedom arise in this framework from the deformation quantization of N -tuple cycles. The large N limit of the gauge theory on D-branes wrapped on a subvariety V of some variety X is geometrically interpreted as the deformation quantization of the formal completion of X along V.