  We propose a method to extend submanifolds, singular Riemannian foliations
and isometric actions from a boundary component of a noncompact symmetric space
to the whole space. This extension method preserves minimal submanifolds,
isoparametric foliations and polar actions, among other properties. One of the
several applications yields the first examples of inhomogeneous isoparametric
hypersurfaces in noncompact symmetric spaces of rank at least two.
