With Carpi, Hillier, Longo and Xu, we study connections between noncommutative geometry and the N=2 super Virasoro nets from the vacuum representations of the Neveu-Schwarz algebra for the central charge in the discrete series c < 3. A universal C*-algebra arises from the N=2 super Virasoro net, and we show that certain DHR sectors give elements of the K0-group of this C*-algebra. We also show that these DHR sectors produce JLO-cocycles in the entire cyclic cohomology of the C*-algebra in the sense of Connes, and compute the index pairing between them. The result gives the Kronecker δ. In this context, we also give a new proof of certain character formulas conjectured by physicists.