KAIMU, Hawaii—Dark igneous rock crunches beneath Garry Hoffeld’s sandals as he crosses the cratered landscape of a remote corner of Hawaii’s Big Island. But he is walking over no ordinary field of hardened lava: This is the site of Hawaii’s Star Visitor Sanctuary and UFO Landing Pad.

Mr. Hoffeld, a member of the Lawful Hawaiian Government, a Hawaiian sovereignty group that seeks independence from the U.S., sees the lava field as a perfect spot for extraterrestrial encounters.

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