  This paper is a continuation of a previous paper in which the first two
authors have introduced the spherical Hecke algebra and the Satake isomorphism
for an untwisted affine Kac-Moody group over a non-archimedian local field. In
this paper we develop the theory of the Iwahori-Hecke algebra associated to
these same groups. The resulting algebra is shown to be closely related to
Cherednik's double affine Hecke algebra. Furthermore, using these results, we
give an explicit description of the affine Satake isomorphism, generalizing
Macdonald's formula for the spherical function in the finite-dimensional case.
