Suppose that (Formula presented.) is a connected reductive algebraic group defined over (Formula presented.), (Formula presented.) is its group of real points, (Formula presented.) is an automorphism of (Formula presented.), and (Formula presented.) is a quasicharacter of (Formula presented.). Kottwitz and Shelstad defined endoscopic data associated to (Formula presented.), and conjectured a matching of orbital integrals between functions on (Formula presented.) and its endoscopic groups. This matching has been proved by Shelstad, and it yields a dual map on stable distributions. We express the values of this dual map on stable tempered characters as a linear combination of twisted characters, under some additional hypotheses on (Formula presented.) and (Formula presented.).

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Keywords spectral transfer, twisted endoscopy
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Journal Journal of the Institute of Mathematics of Jussieu
Mezo, P. (2016). TEMPERED SPECTRAL TRANSFER IN THE TWISTED ENDOSCOPY OF REAL GROUPS. Journal of the Institute of Mathematics of Jussieu, 15(3), 569–612. doi:10.1017/S1474748014000437