The polyelectrolyte layer coating mammalian cells, known as the glycocalyx, may be important in communicating flow information to the cell. In this paper, the layer is modelled as a semi-infinite, doubly periodic array of parallel charged cylinders. The electric potential and ion distributions surrounding such an array are found using the linearized Poisson-Boltzmann equation and an iterative domain decomposition technique. Similar methods are used to calculate Strokes flows, driven either by a shear at infinity or by an electric field, parallel or transverse to the cylinders. The resulting electric streaming currents due to flow over endothelial cells, and the electrophoretic mobilities of red blood cells are deduced as functions of polymer concentration and electrolyte molarity. It is shown that only the top portion of the layer is important in these effects.