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The overlap hypercube fermion is constructed by inserting a lattice fermionwith hypercubic couplings into the overlap formula. One obtains an exactGinsparg-Wilson fermion, which is more complicated than the standard overlapfermion, but which has improved practical properties and is of current interestfor use in numerical simulations. Here we deal with conceptual aspects of theoverlap hypercube Dirac operator. Specifically, we evaluate the axial anomalyand the index, demonstrating that the correct classical continuum limit isrecovered. Our derivation is non-perturbative and therefore valid in alltopological sectors. At the non-perturbative level this result had previouslyonly been shown for the standard overlap Dirac operator with Wilson kernel. Thenew techniques which we develop to accomplish this are of a general nature andhave the potential to be extended to overlap Dirac operators with even moregeneral kernels.Comment: 21 pages, no figures, final version to appear in Eur. Phys. J.

Axial anomaly and index of the overlap hypercube operator