  A subgroup of a Kac-Moody group is called bounded if it is contained in the
intersection of two finite type parabolic subgroups of opposite signs. In this
paper, we study the isomorphisms between Kac-Moody groups over arbitrary fields
of cardinality at least 4, which preserve the set of bounded subgroups. We show
that such an isomorphism between two such Kac-Moody groups induces an
isomorphism between the respective twin root data of these groups. As a
consequence, we obtain the solution of the isomorphism problem for Kac-Moody
groups over finite fields of cardinality at least 4.
