The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary

For any Koszul Artin-Schelter regular algebra A, we consider the universal Hopf algebra aut_(A) 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 aut_(A)=coendU(M). Using this pair (U,M) we show that aut_(A) is quasi-hereditary as a coalgebra and in addition is derived equivalent to the representation category of U.