Twisted cyclic homology of all Podleś quantum spheres

We calculate the twisted Hochschild and cyclic homology of all Podleś quantum spheres relative to diagonal automorphisms. The dimension drop in Hochschild homology is overcome via twisting by the modular automorphism of the canonical SUq(2)SUq(2)-invariant linear functional. Specializing to the standard quantum sphere, we identify the cohomology class of the 2-cocycle discovered by Schmüdgen and Wagner corresponding to the distinguished covariant differential calculus found by Podleś.