Brauer group of moduli stack of stable parabolic PGL(r)-bundles over a curve

Let k be an algebraically closed field of characteristic zero. We prove that the Brauer group of the moduli stack of stable parabolic PGL(r,k)-bundles on a smooth projective curve, with full flag quasi-parabolic structures at an arbitrary parabolic divisor, coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of parabolic PGL(r,k)-bundles. We also compute the Brauer group of the smooth locus of this coarse moduli for more general quasi-parabolic types and weights satisfying certain conditions.