** Coming from the box I have a black, white, and bare. The cooktop has a black, white, red, and green. **
Your power supply sounds to be only a 240 volt circuit. The cooktop on the other hand looks to require a 120/240 volt supply. You may need to have a 120/240 volt line (3-wire + a ground) installed from the fuse panel to connect to the apppliance. Consult with a licensed electrician.