Twisted Cyclic Cohomology and Modular Fredholm Modules

Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515-526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podle\'s spheres and from $SU_q(2)$.