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

Twisted Cyclic Cohomology and Modular Fredholm Modules