A system for implanting a heart valve that includes a radially self-expandable tubular body having an inflow end and an outflow end, and a valve disposed within and attached to the tubular body. A first end of a projection is located at a side surface of the tubular body, and a second free end of the projection defines a groove between the projection and the tubular body. The groove has an opening between the tubular body and the second free end of the projection. Additionally, an elongate outer member is configured to move into the groove and to move heart tissue into the groove, such that the heart tissue is disposed between the tubular body and the projection.
