Greenberg algebras and ramified Witt vectors

Let  be a complete discrete valuation ring of mixed characteristic and with finite residue field k. We study a natural morphism r: R_O→W_{O,k} between the Greenberg algebra of O and the special fiber of the scheme of ramified Witt vectors over O. It is a universal homeomorphism with proinfinitesimal kernel that can be explicitly described in some cases