Free Wreath Product by the Quantum Permutation Group

Let A be a compact quantum group, let nN^* and let A_aut(X_n) be the quantum permutation group on n letters. A free wreath product construction A*_wA_aut(X_n) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.