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 K-homo logy. 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 var iety X is geometrically interpreted as the deformation quantization of the formal completion of X along V.