This paper presents an extensive characterization and modeling of a commercial 28-nm FDSOI CMOS process operating down to cryogenic temperatures. The important cryogenic phenomena influencing this technology are discussed. The low-temperature transfer characteristics including body-biasing are modeled over a wide temperature range (room temperature down to 4.2 K) using the design-oriented simplified-EKV model. The trends of the free-carrier mobilities versus temperature in long and short-narrow devices are extracted from dc measurements down to 1.4 K and 4.2 K respectively, using a recently-proposed method based on the output conductance. A cryogenic-temperature-induced mobility degradation is observed on long pMOS, leading to a maximum hole mobility around 77 K. This work sets the stage for preparing industrial design kits with physics-based cryogenic compact models, a prerequisite for the successful co-integration of FDSOI CMOS circuits with silicon qubits operating at deep-cryogenic temperatures.