algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety complex smooth quasiprojective algebraic variety; complex linear algebraic group; localization; Mayer-Vietoris sequences; higher \(K\)- theory; weakly \(G\)-equivariant \({\mathcal D}_ X\)-modules; Riemann-Roch theorem; derived categories; Thomason's approximation theorem 