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Preheat a well-oiled grill to medium-high heat. Wash and dry produce.
Halve, core, and thinly slice green pepper into strips. Halve, peel, and thinly slice onion. Halve lime crosswise. Thinly slice one half into rounds; quarter the other half. (For 4 servings, thinly slice one lime; quarter the other.)
OVEN ALTERNATIVE: Adjust rack to top position (top and middle positions for 4) and preheat oven to 425 degrees.