Deformed boost transformations that saturate at the Planck scale

We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis κ-Poincaré Hopf algebra. We emphasize the role of these boost transformations in a recently-proposed new relativistic theory, and their relevance for experimental studies presently being planned. We find that when the (dimensionful) deformation parameter is identified with the Planck length, which together with the speed-of-light constant has the status of observer-independent scale in the new relativistic theory, the deformed boosts saturate at the value of momentum that corresponds to the inverse of the Planck length.