One of the conjectural properties of a Langlands correspondence is its compatibility with endoscopic induction. DeBacker and Reeder have recently constructed a partial local Langlands correspondence for p-adic groups, focusing on L-packets consisting of depth-zero supercuspidal representations. In this paper we prove the conjectural endoscopic transfer for these L-packets.
Tasho Kaletha. "Endoscopic character identities for depth-zero supercuspidal -packets." Duke Math. J. 158 (2) 161 - 224, 1 June 2011. https://doi.org/10.1215/00127094-1333995