Heat the olive oil in a large skillet over medium heat. Add the onion and sauté for 3-5 minutes until the onion begins to soften. Add the red pepper and continue cooking for another 3 minutes until the peppers have softened. Add the sugar, salt, pepper and vinegar and simmer until most of the liquid has evaporated, about 5 minutes. Set aside. (Note: The relish can be made up to 3 days in advance. Store in an airtight container in the refrigerator).

Preheat a gas or charcoal grill to medium high heat.

Grill the chorizo sausages, turning occasionally, until they are browned and cooked though, about 15 minutes.

Place a sausage in each of the buns and garnish with arugula and red pepper relish.