Rational Homotopy and Hodge Theory of Moduli Stacks of principal G-bundles

For a semisimple complex algebraic group G we determine the rational cohomology and the Hodge-Tate structure of the moduli stack Bun₆, ₗ of principal G-bundles over a connected smooth complex projective variety X of special type using the homotopy theory of the underlying topological stack.