Preheat the oven to 350°. Spread the coconut in a pie plate; toast for about 5 minutes, or until golden; let cool.
Using a sharp knife, peel the limes, removing the bitter white pith. Working over the jar of a blender, cut in between the membranes to release the sections. Squeeze the juice from the membranes into the blender. Puree the lime sections and juice with the coconut sorbet and yogurt until smooth, about 30 seconds. Pour the frappé into glasses, garnish with the coconut and serve.
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