1. Cut onion into 3/4- to 1-inch-thick slices. Brush both sides of onion slices evenly with olive oil.
2. Grill onion, covered with grill lid, over medium-high heat (350° to 400°) 3 to 4 minutes on each side or until grill marks appear and onion is tender. Transfer to cutting board, and let cool slightly. Coarsely chop onion slices.
3. Toss together onion, feta, and remaining ingredients.