From the MR review: "In this article the authors give methods to compute the Chow groups of schemes provided with a 'sufficiently nice filtration'. Their result has the useful corollary that the Chow groups of a scheme having a cellular decomposition are free with basis [the classes of] the closures of the cells. These results will be most useful in enumerative geometry, where one often encounters schemes with such decompositions. Indeed, the authors give some nice examples with schemes such as U = Hilb³P² − Al³P². Here Hilb³P² is the Hilbert scheme parameterizing triples of points in P² and Al³P² is the subscheme of collinear triples ('Al' stands for 'aligné', which is the French for 'collinear'). If we set U' = Hilb³Pⁿ - Al³Pⁿ and let Gr(2,n) be the Grassmannian of 2-planes in Pⁿ, then there is a map U' → Gr(2,n) which sends a triple of noncollinear points to the unique plane which contains them. This map is locally trivial with fibre U. The authors' results do not quite suffice to compute the Chow groups of U' but they can compute the ranks of these groups and hence the Betti numbers of U'."
MR951648 (89h:14003)