postawić --wię -wisz (pf), (impf) stawiać = to place, locate, stand, pose.
In this context = to stand / foot the bill = to buy something for someone as a treat
postawić --wię -wisz (pf), (impf) stawiać = to place, locate, stand, pose.
In this context = to stand / foot the bill = to buy something for someone as a treat