Grease a 9 x 13 x 2-inch baking pan (2 1/2 to 3-quart size).
Heat oven to 350 F.
Heat the olive oil in a large skillet over medium heat.
When the oil is hot and shimmering, add the ground beef, onions, and celery.
Cook until beef is browned and vegetables are tender, stirring frequently.
Add garlic and peppers; cook, for about 1 minute longer, stirring frequently.
Stir in the tomatoes, chili powder, salt, pepper, and cumin. Bring to a simmer.
In the prepared baking dish, arrange half of the sliced potatoes, then top with half of the corn, half of the ground beef mixture, and half of the cheese.
Repeat the layers, ending with the remaining cheese.
Cover the baking dish tightly with foil and bake for about 1 hour and 15 minutes, or until potatoes are tender.