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Is it correct that Langlands' combinatorial exercise (as he terms it in his paper "Shimura varieties and the Selberg trace formula") is to establish base change identities between orbital integrals of the group $G$ over a number field and twisted orbital integrals over some unramified extension? Or am I completely wrong?

I am trying to understand this part of the Langlands' paper "On the zeta-functions of some simple Shimura varieties" without much success...

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  • $\begingroup$ I think so. My understanding is that he proves a fundamental lemma in the context of base-change. $\endgroup$
    – Emerton
    Commented Oct 22, 2011 at 4:54

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