  Let $\mathbf{G}$ be a reductive Chevalley group scheme (defined over
$\mathbb{Z}$). Let $\mathcal{C}$ be a smooth, projective, geometrically
integral curve over a field $\mathbb{F}$. Let $P$ be a closed point on
$\mathcal{C}$. Let $A$ be the ring of functions that are regular outside
$\lbrace P \rbrace$. The fraction field $k$ of $A$ has a discrete valuation
$\nu=\nu_{P}: k^{\times} \rightarrow \mathbb{Z}$ associated to $P$. In this
work, we study the action of the group $ \textbf{G}(A)$ of $A$-points of
$\mathbf{G}$ on the Bruhat-Tits building
$\mathcal{X}=\mathcal{X}(\textbf{G},k,\nu_{P})$ in order to describe the
structure of the orbit space $ \textbf{G}(A)\backslash \mathcal{X}$. We obtain
that this orbit space is the ``gluing'' of a closed connected CW-complex with
some sector chambers. The latter are parametrized by a set depending on the
Picard group of $\mathcal{C} \smallsetminus \{P\}$ and on the rank of
$\mathbf{G}$. Moreover, we observe that any rational sector face whose tip is a
special vertex contains a subsector face that embeds into this orbit space.
