Heat your outdoor gas or charcoal grill to medium-high heat.
While your grill is heating, mix together the sugar, chili powder, cumin, salt, pepper, and oil to make the rub. Stir it all up into a paste.
Pat the pork loin dry with paper towels. Place it on a pan, and cover the pork with rub on all sides. There shouldn't be any rub leftover when you're done.
Before placing the pork on the hot grill, add a little oil or non-stick grilling spray to the grill grates. Grill the pork loin, on each side for approximately 10 minutes, or until internal temp of the pork reaches 145 degrees F. Slightly pink inside is okay.
After turning the meat, brush 1/2 cup of barbecue sauce on each side of the tenderloin. (Be sure to reserve the remaining 1 cup of sauce for serving.) Remove from the grill, and let rest on a cutting board for 5 minutes.
Thinly slice the pork loin. Place a few slices of pork on a dinner roll with barbecue sauce on top of the pork. Serve immediately while warm.
Refrigerate any leftover pork separate from any bread or sauce in an airtight container.