  In "Elliptic spectra, the Witten genus, and the Theorem of the cube" (Invent.
Math. 146 (2001)), the authors constructed a natural map from the Thom spectrum
MU<6> to any elliptic spectrum, called the "sigma orientation". MU<6> is an
H-infinity ring spectrum, and in this paper we show that if E is a K(2)-local
H-infinity elliptic spectrum, then the sigma orientation is a map of H-infinity
spectra.
