Principal fibrations from noncommutative spheres

We construct noncommutative principal fibrations S-theta(7) -> S-theta(4) which are deformations of the classical SU(2) Hopf fibration over the four sphere. 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. "The algebra inclusion A(S-theta(4)) hooked right arrow A(S-theta(7)) is an example of a not-trivial quantum principal bundle."