Unramified Brauer group of the moduli spaces of $PG{L}_r(\mathbb{C})$-bundles over curves

Let $X$ be an irreducible smooth complex projective curve of genus at least two. Let $N$ be a connected component of the moduli space of semistable principal ${\mathrm{P}\mathrm{G}\mathrm{L}}_r(\mathbb{C})$- bundles over $X$; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of $N$ is trivial.