Salary caps are not God-given. Essentially, they exist to prevent you from single-handedly increaseincreasing one of your subordinate's salary to a disproportional level. Nothing prevents this decision from being taken by involving other people. Talk to your superior and make them aware of the situation.
In the end, if the guy deserves 2x the average salary and you can't pay him that much, he'll have to find a company that can.
Speaking of the attitude, this guy is about as "immature" as the bartender who refuses to give you two beers when you only have paid for one, because your wife decided to set a cap on your bar expenses.