  For a linear group $G$ acting on an absolutely irreducible variety $X$ over
the rationals $\QQ$, we describe the orbits of $X(\QQ_p)$ under $G(\QQ_p)$ and
of $X(\FF_p((t)))$ under $G(\FF_p((t)))$ for $p$ big enough. This allows us to
show that the degree of a wide class of orbital integrals over $\QQ_p$ or
$\FF_p((t))$ is $\leq 0$ for $p$ big enough, and similarly for all finite field
extensions of $\QQ_p$ and $\FF_p((t))$.
