Suppose that $Y$ is a subvariety of $X$, and both are nonsingular. I'm interested in knowing a nice condition to make the inclusion $i\colon Y\to X$ induce an isomorphism of Chow rings $A^{.}(X)\cong A^{.}(Y)$. For example, if $X$ and $Y$ were spaces and I wanted an isomorphism in cohomology, I might hope to show that $Y$ is a deformation retract of $X$.

So my novice question (not very precise, sorry) is if intersection theory offers an analogous or at least comparably useful technique. I'd appreciate a pointer to an example, say, in Fulton's book. (Which, if I'd read and understood fully, of course, surely I could answer my own question!)