We will investigate in the simplest setting, how an``R-matrix'' (the building block of ``quantum integrable systems'') is attached to the equivariant cohomology of Grassmannians. We will compute the R-matrix in the case of CP^1 and discuss how the result generalizes to arbitrary Grassmannians. As an application, we shall derive the AJSBilley formula (restriction of Schubert classes to fixed points).