A short proof of the Selberg principle for a \(p\)-adic group (Q2701603)

Let \(F\) be a local field of characteristic zero, \(G\) be the group of \(F\)-points of a reductive algebraic group defined over \(F\). The ``abstract Selberg principle'' proved by \textit{P. Blanc} and \textit{J.-L. Brylinski} [J. Funct. Anal. 109, 289-330 (1992; Zbl 0783.55004)] states that the orbital integrals of the Hattori rank of a finitely generated projective smooth representation of \(G\) over the conjugacy classes of the non-compact elements vanish. NEWLINENEWLINENEWLINEThe author gives a new proof based on Clozel's integration formula [\textit{L. Clozel}, Ann. Math. (2) 129, 237-251 (1989; Zbl 0675.22007)] and some \(K\)-theoretic arguments.