Chern-Connes character for the invariant Dirac operator in odd dimensions (Q882956)

A proof of the Lefschetz fixed point formula of Freed for an orientation-reversing involution on an odd dimensional spin manifold is presented using a direct method introduced in [\textit{J. D. Lafferty, Y. Yu} and \textit{W. Zhang}, Trans. Am. Math. Soc. 329, No. 2, 571--583 (1992; Zbl 0747.58016)]. Moreover, the author constructs an even spectral triple by the Dirac operator and the orientation-reversing involution and computes the Chern-Connes character for this spectral triple.