Basic functions and the stable trace formula

Basic functions are noncompactly supported test functions that allow one to weight the Arthur-Selberg trace formula with automorphic L-functions, which is useful in studying Langlands functoriality beyond endoscopic cases. Work of Finis, Lapid, and Müller allow the use of such test functions in the coarse non-invariant trace formula. I will report on work in progress extending this to the invariant and stable trace formulas.