The endoscopic character identity for even special orthogonal groups

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.