  In this paper, we use localization algebras to study higher rho invariants of
closed spin manifolds with positive scalar curvature metrics. The higher rho
invariant is a secondary invariant and is closely related to positive scalar
curvature problems. The main result of the paper connects the higher index of
the Dirac operator on a spin manifold with boundary to the higher rho invariant
of the Dirac operator on the boundary, where the boundary is endowed with a
positive scalar curvature metric. Our result extends a theorem of Piazza and
Schick.
