  We construct new examples of ergodic coactions of compact quantum groups, in
which the multiplicity of an irreducible corepresentation can be strictly
larger than the dimension of the latter. These examples are obtained using a
bijective correspondence between certain ergodic coactions on C*-algebras and
unitary fiber functors on the representation category of a compact quantum
group. We classify these unitary fiber functors on the universal orthogonal and
unitary quantum groups. The associated C*-algebras and von Neumann algebras can
be defined by generators and relations, but are not yet well understood.
