Algebraic rational cells and equivariant intersection theory

We provide a notion of algebraic rational cell with applications to intersection theory on singular varieties with torus action. Based on this notion, we study $$\mathbb {Q}$$Q-filtrable varieties: algebraic varieties where a torus acts with isolated fixed points, such that the associated Białynicki-Birula decomposition consists of algebraic rational cells. We show that the rational equivariant Chow group of any $$\mathbb {Q}$$Q-filtrable variety is freely generated by the classes of the cell closures. We apply this result to group embeddings, and more generally to spherical varieties.