Let R be a finitely generated integral algebra over C, so that Spec(R)=X is an affine variety over C. An action of G=C∗ on Spec(R) is equivalent to a Z-grading of R over C, say R=⊕i∈ZRi. To study the GIT quotients X//G linearised on the trivial bundle, choose any n∈Z and define a Z-grading on R[z] by Ri⊂R[z]i, z∈R[z]−n. As X=Spec(R)=Proj(R[z]), this Z-grading is equivalent to a linearisation on the trivial bundle \mc{O} of the G-action of X. The quotient is then Proj(R[z]G)=Proj(R[z]0)=Proj⊕i∈NRnizi.