ABU DHABI—News Corp.'s Fox International Channels said Monday it is basing the Middle East operations of its global online advertising network in Abu Dhabi and setting up an office here for its documentary-production arm. Fox International said it would also move some broadcasting operations related to its Mideast channels from Hong Kong and other locations to Abu Dhabi. The moves are the latest by a handful of large, international media outlets to establish footholds in Abu Dhabi, the capital of the United Arab Emirates. The city-state, in an effort to diversify away from oil, has set out to lure a...