Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network controlling growth and division, and couple this to the physical forces arising within the cell collective. We analyse this model using both particle-based computer simulations and a continuum theory. We focus on 2D colonies confined in a channel. These develop moving growth fronts of dividing cells with quiescent cells in the interior. The profile and speed of these fronts are non-trivially related to the substrate friction and the cell cycle parameters, providing a possible approach to measure such parameters in experiments.