  Let $G$ be a split connected reductive group over $\mathbb{Z}$. Let $F$ be a
non-archimedean local field. With $K_m: = Ker(G(\mathfrak{O}_F) \rightarrow
G(\mathfrak{O}_F/\mathfrak{p}_F^m))$, Kazhdan proved that for a field
$F'$sufficiently close local field to $F$, the Hecke algebras
$\mathcal{H}(G(F),K_m)$ and $\mathcal{H}(G(F'),K_m')$ are isomorphic, where
$K_m'$ denotes the corresponding object over $F'$. In this article, we
generalize this result to general connected reductive groups.
