Extensions of tempered representations

Let pi, pi' be irreducible tempered representations of an affine Hecke algebra with positive parameters. We compute the higher extension groups Ext explicitly in terms of the representations of analytic R-groups corresponding to pi and pi'. The result has immediate applications to the computation of the Euler-Poincar, pairing EP (pi, pi'), the alternating sum of the dimensions of the Ext-groups. The resulting formula for EP(pi, pi') is equal to Arthur's formula for the elliptic pairing of tempered characters in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over non-archimedean local fields of arbitrary characteristic. This sheds new light on the formula of Arthur and gives a new proof of Kazhdan's orthogonality conjecture for the Euler-Poincar, pairing of admissible characters.