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

$\ell$-adic Poisson Formula and Endoscopy for $p$-Adic Reductive Groups