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We prove a generalization of Harish-Chandra's character orthogonalityrelations for discrete series to arbitrary Harish-Chandra modules for realreductive Lie groups. This result is an analogue of a conjecture by Kazhdan for$\mathfrak p$-adic reductive groups proved by Bezrukavnikov, and Schneider andStuhler.

Kazhdan's orthogonality conjecture for real reductive groups