The present invention relates to an exhaust-gas heat exchanger for a motor vehicle, having an encircling heat exchanger duct with a bypass pipe situated at the inside, a control flap being provided for conducting an exhaust-gas flow through the heat exchanger duct or through the bypass pipe, said exhaust-gas heat exchanger being characterized in that the control flap has an opening with a pipe stub-like section, the pipe stub-like section being in flow-conducting contact with an inlet opening of the bypass pipe in a bypass position, and the control flap being rotatable from a bypass position into a transfer position, in which the inlet is closed.