  We study the representation theory of quantizations of Gieseker moduli
spaces. Namely, we prove the localization theorems for these algebras, describe
their finite dimensional representations and two-sided ideals as well as their
categories O in some special cases. We apply this to prove our conjecture with
Bezrukavnikov on the number of finite dimensional irreducible representations
of quantized quiver varieties for quivers of affine type.
