  For a finite abelian group G in GL(n,k), we describe the coherent component
Y_theta of the moduli space M_theta of theta-stable McKay quiver
representations. This is a not-necessarily-normal toric variety that admits a
projective birational morphism to A^n/G obtained by variation of GIT quotient.
As a special case, this gives a new construction of Nakamura's G-Hilbert scheme
that avoids the (typically highly singular) Hilbert scheme of |G|-points in
A^n. To conclude, we describe the toric fan of Y_theta and hence calculate the
quiver representation corresponding to any point of Y_theta.
