Shortly after takeoff, the crew of the Boeing 767 were advised by ATC that tyre debris and part of a control pulley had been found on the departure runway. The crew advised that they would return to land after jettisoning fuel to reach maximum landing weight. The crew later declared an emergency due to aircraft control difficulties. A distress phase was initiated by ATC. When emergency services were in position, the airport was closed to all other operations and the aircraft landed safely. A subsequent inspection of the aircraft revealed that the tread of the inner rear tyre on the right main landing gear had separated, although the tyre had remained inflated. Liberated rubber debris had entered the right wheel well, damaging a pulley and its mounting bracket in the right inboard aileron control system. This led to a loss of function of the right inboard aileron due to a reduction of aileron cable tension. Investigation of the tyre failure by the tyre manufacturer concluded that the failure was the result of the loss of rubber adhesion to the casing plies below the buff line. The tyre was on its fifth retread and had been subjected to nine landings since the last retread. The aircraft manufacturer reported that redundancies built into the aircraft control system provided sufficient remaining lateral control, despite the loss of right inboard aileron function.