  We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody
group over a local non-archimedian field. We prove a generalization of the
Satake isomorphism for these algebras, relating it to integrable
representations of the Langlands dual affine Kac-Moody group. In the next
publication we shall use these results to define and study the notion of Hecke
eigenfunction for the group $G_{\aff}$
