  We study the moduli space of twisted quasimaps from a fixed smooth projective
curve to a Nakajima's quiver variety and the moduli space of $\delta$-stable
framed twisted quiver bundles with moment map relations. We show that they
carry symmetric obstruction theories and when $\delta$ is large enough, they
exactly coincide. These results generalize works of D.E. Diaconescu about the
ADHM quiver, in the framework of the quasimap theory of I. Ciocan-Fontanine, D.
Maulik and the author.
