2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154594In this paper we produce several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric projections. In the CR setting these operators arise from the Kohn-Rossi complex and include the Szegö projections on forms. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.v4: new CR invariants with coefficients in CR holomorphic vector bundles + more comments about computation of the invariants + new title; 32 pagesDifferential GeometryComplex VariablesPrimary 32A25; Secondary 32V20, 53D35, 58J40, 58J42text