I do not recall the brand of belt in my 2006 Agility 50 but I seriously doubt Dayco as oem on any Kymco. The picture of the shredded belt suggests excessive heat. Heat is normal for all "rubber band" CVT's but excessive heat is from slippage. Belt slip can be from wrong "V" angle of belt (wrong belt), too long or too short a belt maybe, improper assembly of front pulley or incorrect spring in rear pulley.
My first recommendation is reliably determine what the original belt was and get an original replacement. Second, make ABSOLUTELY SURE on the front pulley the washer between the sleeve and the engine, next to the engine has the inner diameter chamfer NEXT to the engine side. Third, check the color of the big spring on the rear pulley (not clutch shoe springs--they are little). I think mine was white but verify with a reputable dealer or authentic parts diagram. Finally, back up on the front pulley, the most common mistake is not getting the stationary (outer) plate/pulley half seated COMPLETELY before tightening the nut. This usually destroys the front pulley. It may be able to destroy the belt as well.
