A system for implanting a heart valve includes a radially self-expandable tubular body having an inflow end and an outflow end and a preformed groove disposed at an outer surface of the tubular body between the inflow end and the outflow end. The preformed groove extends at least partially around the tubular body and has a circumferential opening facing radially outward of the tubular body. A valve is disposed within and is attached to the tubular body, and an elongate outer member is configured to form a loop encircling the preformed groove so as to guide portions of native valve leaflets and/or chords into the preformed groove. The outflow end of the tubular body includes a frustoconical shape that slopes radially outward from the preformed groove toward the outflow end when the outflow end but not the inflow end has been released from a delivery catheter.
