Cell phone antenna booster

I need to boost my handheld cell phone signal for good reception at home. I want to place a direcitonal antenna on the roof and run a low loss cable downstairs. Getting or making an antenna is trivial. But how does one connect the antenna cable to the cell phone. There is no "connector" for the stubby existing phone antenna to connect to, just a single screw thread. So I could connect the center wire of a coax cable to that screw thread, but there is no way to connect the ground return shield.

Has anyone seen any sort of resonating or capacitive sleeve that one could place over the existing cell antenna that would properly launch a nice tem wave onto the inside of the coax cable?

Buy a car kit for your phone.