Riemannian metrics of positive scalar curvature on compact manifolds with boundary

We prove that any metric of positive scalar curvature on a manifold X extends to the trace of any surgery in codim > 2 on X to a metric of positive scalar curvature which is product near the boundary. This provides a direct way to construct metrics of positive scalar curvature on compact manifolds with boundary. We also show that the set of concordance classes of all metrics with positive scalar curvature on S ⁿ is a group.