A formula of Arthur and affine Hecke algebras

Let $π, π'$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincaré pairing $EP (π,π')$, the alternating sum of the dimensions of the Ext-groups. We show that $EP (π,π')$ can be expressed in a simple formula involving an analytic R-group, analogous to a formula of Arthur in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over nonarchimedean local fields of arbitrary characteristic.

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