  Let $K/\mathbb Q_{p}$ be a finite extension with ring of integers $o$, let
$G$ be a connected reductive split $\mathbb Q_{p}$-group of Borel subgroup
$P=TN$ and let $\alpha$ be a simple root of $T$ in $N$. We associate to a
finitely generated module $D$ over the Fontaine ring over $o $ endowed with a
semilinear \'etale action of the monoid $T_{+} $ (acting on the Fontaine ring
via $\alpha$), a $G(\mathbb Q_{p})$-equivariant sheaf of $o$-modules on the
compact space $G(\mathbb Q_{p})/P(\mathbb Q_{p})$. Our construction generalizes
the representation $D\boxtimes \mathbb P^{1} $ of $ GL(2,\mathbb Q_{p})$
associated by Colmez to a $(\varphi,\Gamma)$-module $D$ endowed with a
character of $\mathbb Q_{p}^{*}$.
