For any Koszul Artin–Schelter regular algebra A , we consider the universal Hopf algebra coacting on A , introduced by Manin. To study the representations (i.e. finite dimensional comodules) of this Hopf algebra, we use the Tannaka–Krein formalism. Specifically, we construct an explicit combinatorial rigid monoidal category U, equipped with a functor M to finite dimensional vector spaces such that . Using this pair (U,M) we show that is quasi-hereditary as a coalgebra and in addition is derived equivalent to the representation category of U.