A system for implanting a heart valve (1) incudes a railly self-expandable tubular body (30) having an inflow end and an outflow end and a projection (55) extending from a side surface of the tubular body toward the inflow end. The system further includes a valve (40) disposed within and attached to the tubular body, and may include fabric (120) that forms a pouch (122) between the tubular body and the projection.
