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Add arugula and roasted red peppers to the center of the wrap.
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In a medium bowl, toss chicken with Caesar salad dressing and season with salt and pepper. Stir in diced apples.
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Spoon chicken mixture evenly onto the center of the wrap and sprinkle with freshly grated Parmesan.
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Roll wrap up and cut in half. Serve with extra dressing, if desired.