A transcatheter atrio-ventricular valve prosthesis for functional replacement of an atrio-ventricular heart valve in a connection channel, the prosthesis comprising a radially expandable tubular body extending along an axis, and a valve arranged within and attached to the tubular body. The tubular body is provided with an outer circumferential groove which is open to the radial outside of the tubular body, whereby the tubular body is separated by the outer circumferential groove into first and second body sections. The tubular body is provided with a first plurality of projections which extend from the first or second body section in an axial direction of the tubular body and each of which has a free end arranged to overlap the outer circumferential groove. An elongate outer member may be disposed at the exterior of the connection channel wall structure at a level of the circumferential groove.
