The present invention relates to an assembly comprising: a ring having anchoring elements for attaching the ring in a passage surrounded by body tissue, in particular blood vessel tissue. An applicator for fitting the ring in the passage; in which the anchoring elements have an anchoring position in which they protrude with respect to the ring, and in which the anchoring elements comprise a memory material, such as a memory metal or memory polymer, and are designed so that they can be bent from an anchoring position counter to a spring force into a fitting position and can be frozen in this fitting position by a temperature treatment in order to bend the anchoring elements back from the fitting position by the effect of this spring force into the anchoring position when a predetermined threshold temperature is exceeded, and in which the applicator is provided distally with a carrier for carrying the ring. The assembly according to the invention is provided with an influencing system for influencing the temperature of the anchoring elements of the ring carried by the carrier in such a way that the anchoring elements bend back from the fitting position to the anchoring position by increasing the temperature of the anchoring elements to above the threshold temperature.