In a foreign manner; with foreign characteristics or in the manner of a foreigner; in a way that is foreign or strange to the speaker.
From 'foreign' plus the adverbial suffix '-ly' from Old English '-lice.' This forms an adverb expressing manner or quality.
Adding '-ly' to 'foreign' to make an adverb is technically correct but sounds awkward—most speakers say 'in a foreign way' instead, showing how some grammatically valid words just feel unnatural to language users.
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