Fearing that Germany might use Iceland as a base for U-boats and the Luftwaffe, Britain had offered the Icelanders the chance to enter the war on Britain’s side. When the offer was rejected, Britain invaded and occupied the island.
Anxious to use its troops elsewhere, the British persuaded the Icelandic parliament to accept American occupation—and Roosevelt obliged. The Americans were to remain in Iceland for the duration of World War II.
I sure the Icelanders went to great lengths to keep the GI’s away from their daughters!