Braided quantum symmetries of graph C∗-algebras

We prove the existence of a universal braided compact quantum group acting on a graph Formula: see text-algebra in the category of Formula: see text-Formula: see text-algebras with a twisted monoidal structure, in the spirit of the seminal work of Wang. To achieve this, we construct a braided analogue of the free unitary quantum group and study its bosonization. As a concrete example, we compute this universal braided compact quantum group for the Cuntz algebra.