The Rosenberg index is a powerful obstruction for a closed spin manifold to admit a metric with positive scalar curvature (psc). Inspired by the result of Gromov-Lawson, Hanke-Pape-Schick prove that the Rosenberg index of a codimension 2 submanifold N of M (with some assumptions on lower homotopy groups) obstructs the existence of a psc metric on M. In this talk we introduce a refinement of the Hanke-Pape-Schick theorem, which relates the Rosenberg index of N with that of M. This is a joint work with Thomas Schick.