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We calculate the equivariant index formula for an infinite dimensional Clifford module canonically associated with any closed oriented Riemannian manifold. It encompasses the fractional index formula of the projective Dirac operators by Mathai-Melrose-Singer. Our method can be regarded as the calculation of a topological index for such operators.doi:10.1090/s0002-9939-2013-11588-1 fatcat:djluz26qobatlipqgcjlur5jve