Hopf-dihedral (co)homology and L-theory

We develop an appropriate dihedral extension of the Connes-Moscovici characteristic map for Hopf ∗-algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial L-theory classes of a ∗-algebra that carry a Hopf symmetry over a Hopf ∗-algebra. Using our machinery we detect a previously unknown L-class of the standard Podles sphere.