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In this paper, we consider a certain sequence of homogeneous flat vectorbundles on a compact locally symmetric orbifold, and we compute explicitly theassociated asymptotic Ray-Singer analytic torsion. The basic idea is convertingthis question via the Selberg's trace formula into computing the semisimpleorbital integrals. Then the central part is to evaluate the elliptic orbitalintegrals which are not identity orbital integrals. For that purpose, we deducea geometric localization formula, so that we can rewrite an elliptic orbitalintegral as a sum of certain identity orbital integrals associated with asmaller Lie group. The explicit geometric formula of Bismut for semisimpleorbital integrals plays an essential role in these computations.

On full asymptotics of analytic torsions for compact locally symmetric orbifolds