Projective normality of G.I.T. quotient varieties modulo finite groups

We prove that for any finite dimensional representation V of a finite group G of order n the quotient variety G??(V) is projectively normal with respect to descent of 𝒪(1)^?l where l = lcm{1,2,3,4,…,n}. We also prove that for the tautological representation V of the alternating group A_n the projective variety A_n??(V) is projectively normal with respect to the descent of the above line bundle.