algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety Adams-Novikov spectral sequence; stable homotopy groups of spheres; Adams spectral sequence; Brown-Peterson homology; Lambda-algebra; complex bordism; formal group law theory; periodic family; chromatic spectral sequence; Morava K-theories; Kervaire invariant 1 elements; Hopf- algebroids; Massey products; Steenrod powers 