Abstract We establish the endoscopic character identity for certain bounded 𝐴-packets of non-quasisplit even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasisplit case to the quasisplit case and the real Adams–Johnson case by combining the local-global compatibility principle with Arthur’s multiplicity formula for non-quasisplit global even special orthogonal groups established by Chen and Zou. This result plays a key role in the author’s work on the compatibility between the Fargues–Scholze local Langlands correspondence and the classical local Langlands correspondence for even special orthogonal groups.
Hao Peng (Tue,) studied this question.