The cell-supported lipid bilayer (SLB) adhesion system has been widely used as the model system to study the receptor-ligand interactions that occur at the membrane interface. The ligand-functionalized SLBs are deposited either directly on solids or on polymer cushions. An important question that arises is whether the geometry of the SLB affects the binding of cell adhesion receptors to the ligands. By using a mesoscopic mechanical model and Monte Carlo simulations, we have investigated the adhesion of a fluid membrane to a corrugated or egg-carton shaped SLB. We find that the nanoscale geometry of the SLB strongly affects the receptor-ligand binding. This effect results from the fact that the adhering membrane bends according to the SLB geometry in order for the adhesion receptors to bind ligands. The membrane bending couples with spatial distribution of the receptor-ligand complexes and membrane thermal undulations. Our results demonstrate that cell adhesion to SLBs can be controlled by tuning the nanoscale geometry of the SLB, and may have profound implications for future development of tissue engineering and regenerative medicine.