Abstract
Let G+ be the group of real points of a possibly disconnected linear reductive algebraic group defined over R which is generated by the real points of a connected component G'. Let K be a maximal compact subgroup of the group of real points of the identity component of this algebraic group. We characterize the space of maps π↦tr(π(f)), where π is an irreducible tempered representation of G+ and f varies over the space of smooth, compactly supported functions on G' which are left and right K-finite. This work is motivated by applications to the twisted Arthur-Selberg trace formula
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