  Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and
$\varpi$ be an indeterminate. In order to study
$\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and
$\mathfrak{G}(\mathbb{k}(\varpi))$, one can make them act on their twin
building $\mathcal{I} = \mathcal{I}_\oplus\times \mathcal{I}_\ominus$, where
$\mathcal{I}_\oplus$ and $\mathcal{I}_\ominus$ are related via a
''codistance''. Masures are generalizations of Bruhat-Tits buildings adapted to
the study of Kac-Moody groups over valued fields. Motivated by the work of
Dinakar Muthiah on Kazhdan-Lusztig polynomials associated with Kac-Moody
groups, we study the action of $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$
and $\mathfrak{G}(\mathbb{k}(\varpi,\varpi^{-1}))$ on their ''twin masure'',
when $\mathfrak{G}$ is a split Kac-Moody group instead of a reductive group.
