  Let G denote a connected reductive group over a nonarchimedean local field F.
Let K denote a special maximal parahoric subgroup of G(F). We establish a
Satake isomorphism for the Hecke algebra H of K-bi-invariant compactly
supported functions on G(F). The key ingredient is a Cartan decomposition
describing the double coset space K\G(F)/K. We also describe how our results
relate to the treatment of Cartier, where K is replaced by a special maximal
compact open subgroup K' of G(F) and where a Satake isomorphism is established
for the Hecke algebra of K'-bi-invariant compactly supported functions on G(F).
