Preheat the grill to medium-high. Prepare the peppers and red onion for grilling. If you have mesh mats for grilling vegetables, you can slice the peppers and onion into strips since they won't fall through the grates. If you don't have mesh mats, spray the grill grates with cooking spray or brush with oil. Slice the peppers in half and the onion crosswise into rings (keep the rings intact) so that you have larger pieces to grill. Toss the peppers and onion in the olive oil, garlic powder, cumin, chili powder, salt, and pepper. Grill the veggies for 5 to 10 minutes, turning halfway through, until tender and slightly charred. Remove and set aside. If you grilled bigger pieces of peppers and onions, cut them into strips.
Assemble the quesadillas before putting them on the grill. Brush one side of each tortilla with a little olive oil (the side that will be on the grill). Start by sprinkling cheese on one half of the inside of a tortilla. Spoon some grilled veggies, beans, and corn on top of the cheese, then add another layer of cheese. Fold the tortilla in half. Repeat until you have all of the quesadillas prepared. Even though it's tempting to just add the fillings to the tortilla once it's on the grill, it's difficult to do without burning yourself!
Place the quesadillas on the grill, and cook for about 3 minutes on each side until the cheese is melted and the tortilla has crisped up to your liking. Remove the quesadillas, and cut them into quarters.
Serve with toppings of choice, and enjoy!