We construct noncommutative principal fibrations over a 4-sphere which are deformations of the classical SU(2) Hopf fibration. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula.
