A system for implanting a heart valve, comprising: 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 extending at least partially around the tubular body and having a circumferential opening facing radially outward of the tubular body and a groove bottom; wherein the tubular body further includes a plurality of projections (50; 55) each of which having a first end connected to the tubular body and a second end forming a free end (60; 65) unattached to the tubular body and overlapping with the groove; and wherein the second end of the projections (50; 55) includes a substantially flat end extending in a direction parallel to a tangent to the tubular body; a valve disposed within and attached to the tubular body; and a trapping member configured to be disposed within die preformed groove on the outer surface of the tubular body, the trapping member configured to form at least a partial loop around the tubular body, wherein (i) the circumferential opening of the preformed groove is relatively larger when the outflow end of the tubular body has been deployed from a catheter and the inflow end of the tubular body is disposed within the catheter, and (ii) the circumferential opening of the preformed groove is relatively smaller when the outflow end and the inflow end are fully deployed from the catheter. 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 extending at least partially around the tubular body and having a circumferential opening facing radially outward of the tubular body and a groove bottom; wherein the tubular body further includes a plurality of projections (50; 55) each of which having a first end connected to the tubular body and a second end forming a free end (60; 65) unattached to the tubular body and overlapping with the groove; and wherein the second end of the projections (50; 55) includes a substantially flat end extending in a direction parallel to a tangent to the tubular body; a valve disposed within and attached to the tubular body; and a trapping member configured to be disposed within die preformed groove on the outer surface of the tubular body, the trapping member configured to form at least a partial loop around the tubular body, wherein (i) the circumferential opening of the preformed groove is relatively larger when the outflow end of the tubular body has been deployed from a catheter and the inflow end of the tubular body is disposed within the catheter, and (ii) the circumferential opening of the preformed groove is relatively smaller when the outflow end and the inflow end are fully deployed from the catheter. (i) the circumferential opening of the preformed groove is relatively larger when the outflow end of the tubular body has been deployed from a catheter and the inflow end of the tubular body is disposed within the catheter, and (ii) the circumferential opening of the preformed groove is relatively smaller when the outflow end and the inflow end are fully deployed from the catheter.