The private pilot stated that he was conducting a full stop landing. He executed a normal landing, lowered the tail and was rolling fast. The airplane was on the center line with 300 to 400 feet of runway remaining. He stated that he applied the brakes aggressively, which lifted the tail, and caused the propeller to strike the ground. The aircraft then flipped over and came to rest inverted substantially damaging the vertical stabilizer and wings. Post accident examination by a Federal Aviation Administration inspector revealed no mechanical malfunctions or anomalies that would have precluded normal operation.