Preheat the oven to 350 degrees F (175 degrees C). Place yams on a baking sheet.
Bake yams for 40 minutes, or until tender, turning occasionally. Set aside.
In a medium bowl, mix together the red pepper, avocado, cilantro, olive oil, green onions, cumin and lime juice.
Cut yams in half lengthwise, and fluff the centers with a fork. Top with the avocado stuffing. Season with salt and pepper, and top with shredded Cheddar cheese.