  We compute the $ K $-theory of quantum automorphism groups of finite
dimensional $ C^* $-algebras in the sense of Wang. The results show in
particular that the $ C^* $-algebras of functions on the quantum permutation
groups $ S_n^+ $ are pairwise non-isomorphic for different values of $ n $.
Along the way we discuss some general facts regarding torsion in discrete
quantum groups. In fact, the duals of quantum automorphism groups are the most
basic examples of discrete quantum groups exhibiting genuine quantum torsion
phenomena.
