Spherical varieties are varieties with reductive group actions containing dense orbits of Borel subgroups; there are many important examples including all flag manifolds and toric varieties. This paper gives a finite presentation for the Chow homology groups of any variety \(X\) on which a connected solvable linear algebraic group (for example a Borel subgroup of a reductive group) acts with only finitely many orbits. The authors show that the Künneth map \[A_ * (X) \otimes A_ * (Y) \to A_ * (X \times Y)\] is then an isomorphism for any scheme \(Y\). In addition if \(X\) is complete they give a method to compute the operational Chow cohomology groups of \(X\) (the Kronecker duality map is shown to be an isomorphism).

Reviewer: F.Kirwan (Oxford)