  We build compact moduli spaces of Grassmannian framed bundles over a Riemann
surface, essentially replacing a group by its bi-invariant compactification. We
do this both in the algebraic and symplectic settings, and prove a
Hitchin-Kobayashi correspondence between the two. The spaces are universal
spaces for parabolic bundles, and the reduction to parabolic bundles commutes
with the correspondence. An analogous correspondence is outlined for the
generalized parabolic bundles of Bhosle.
