algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety Complex semisimple group; quantized enveloping algebra at a root of unity; cohomology; tilting module; principal block; support; two-sided cell; affine Weyl group; nilpotent cone; Springer resolution; equivariant coherent sheaf; orbit; equivariant vector bundle 