to emit / to give off / to send out (or up, forth) / to brave / to face / reckless / to falsely adopt (sb's identity etc) / to feign / (literary) to cover
apex / crown of the head / top / roof / most / to carry on the head / to push to the top / to go against / to replace / to substitute / to be subjected to (an aerial bombing, hailstorm etc) / (slang) to "bump" a forum thread to raise its profile / classifier for headwear, hats, veils etc