  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 the algebraic analogue of $\mathbb{Q}$-filtrable varieties:
algebraic varieties where a torus acts with isolated fixed points, such that
the associated Bialynicki-Birula decomposition consists of algebraic rational
cells. We show that the rational equivariant Chow group of any
$\mathbb{Q}$-filtrable variety is freely generated by the cell closures. We
apply this result to group embeddings, and more generally to spherical
varieties. This paper is an extension of arxiv.org/abs/1112.0365 to equivariant
Chow groups.
