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Generalizing work of Gross--Zagier and Schofer on singular moduli, we studythe CM values of regularized theta lifts of harmonic Whittaker forms. Wecompute the archimedian part of the height pairing of arithmetic specialdivisors and CM cycles on Shimura varieties associated to certain quadraticspaces over an arbitrary totally real base field. As a special case, we obtainan explicit formula for the norms of the CM values of those meromorphic modularforms arising as regularized theta lifts of holomorphic Whittaker forms.

CM values of automorphic Green functions on orthogonal groups over totally real fields