  For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of
the Poisson formula for reductive $p$-adic groups. In order to do this we write
an identity for the trace of regular representation and orbital integrals. Next
we reduce them to orbital integrals for endoscopy groups and look at this as
the special value of $L$-function at $s=0$. And finally show that it is equal
to the special value of motivic $L$-function at $s=0$.
