  We construct a model of spin-Hall effect on a noncommutative 4 sphere with
isospin degrees of freedom (coming from a noncommutative instanton) and
invariance under a quantum orthogonal group. The corresponding representation
theory allows to explicitly diagonalize the Hamiltonian and construct the
ground state; there are both integer and fractional excitations. Similar models
exist on higher dimensional noncommutative spheres and noncommutative
projective spaces.
