  We consider equivariant dimensional reduction of Yang-Mills theory on K"ahler
manifolds of the form M times CP^1 times CP^1. This induces a rank two quiver
gauge theory on M which can be formulated as a Yang-Mills theory of graded
connections on M. The reduction of the Yang-Mills equations on M times CP^1
times CP^1 induces quiver gauge theory equations on M and quiver vortex
equations in the BPS sector. When M is the noncommutative space R_theta^{2n}
both BPS and non-BPS solutions are obtained, and interpreted as states of
D-branes. Using the graded connection formalism, we assign D0-brane charges in
equivariant K-theory to the quiver vortex configurations. Some categorical
properties of these quiver brane configurations are also described in terms of
the corresponding quiver representations.
