We present quantum-scattering calculations of He-4 and He-3 colliding with Rb-87(2). For both helium isotopes, the elastic and inelastic rate coefficients are strongly influenced by the J = 1 partial wave. For the lighter isotope, a strong resonance feature of the J = 1 partial wave is responsible for an extremely efficient vibrational relaxation process. We also perform bound-state calculations of the Rb2He complex for even Rb permutation symmetry and nonzero total angular momentum. The global Rb2He (3)Sigma(+)(u) potential-energy surface used supports four bound states for He-4 and a single one for He-3. We propose an analysis of the (Rb2He)-Rb-87-He-4 spectrum separating the contributions of Rb-2 rotation and helium motion.