I Example in classical case:

Study representation theory of quantum groups using techniques from noncommutative geometry. I Construction of quantum homogeneous spaces and quantum group equivariant vector bundles. I Realization of irreducible representations of quantum groups on cohomology groups of equivariant quantum homogeneous vector bundles. Consider only type-(1,..., 1) modules for quantum groups. R. B. Zhang Equivariant Quantum Vector Bundles Real setting for homogeneous space