  We show how the coupling of gravitinos and gauginos to fluxes modifies
anomaly cancellation in M-theory on a manifold with boundary. Anomaly
cancellation continues to hold, after a shift of the definition of the gauge
currents by a local gauge invariant expression in the curvatures and E8
fieldstrengths. We compute the first nontrivial correction of this kind.
Warning: Ian Moss has called into question several of the numerical
coefficients in the extended Dirac operators in this paper. We have not
confirmed this but the reader is warned not to trust the precise coefficients
in the formulae for the Dirac operators and heat kernel expansions. We believe
these possible errors do not change our qualitative conclusions. One of us
intends to return to the issue and recheck the formulae. We thank Ian Moss for
pointing out these problems.
