  For a split Kac-Moody group (in J. Tits' definition) over a field endowed
with a real valuation, we build an ordered affine hovel on which the group
acts. This construction generalizes the one already done by S. Gaussent and the
author when the residue field contains the complex field [Annales Fourier, 58
(2008), 2605-2657] and the one by F. Bruhat and J. Tits when the group is
reductive. We prove that this hovel has all properties of ordered affine hovels
(masures affines ordonn\'ees) as defined in [Rousseau, ArXiv 0810.4241]. We use
the maximal Kac-Moody group as defined by O. Mathieu and we prove a few new
results about it over any field; in particular we prove, in some cases, a
simplicity result for this group.
