In food processor, combine butter and red pepper; process until fairly smooth.
Spoon butter mixture onto piece of plastic wrap or waxed paper.
Shape butter into 1 in (2.5 cm) thick log.
Wrap tightly; refrigerate 2 hours or until firm. (Butter can be prepared ahead; refrigerate up to 3 days. Let stand at room temperature 20 minutes before serving.)
One hour before serving, put corn in very large bowl of lightly salted cold water; set aside to soak.
Drain corn then place on oiled barbecue grill.
Grill over high heat 15 to 20 minutes, turning often, until husks blacken and corn is tender.
Let corn cool slightly before shucking.
Cut butter into thin slices; serve corn with slices of flavored butter.