Most invertors are 200-400W. Chip pans are normally 3000W.
Besides, most ciggy lighter sockets only output 120W (10A) and alternators only output 80-100A, so you'd probably burn the alternator out trying to fry your chips.
There are bigger 12v inverters 1500 to 3000W, these are usualy for boats which have banks of bigger batterys. A 1500 W inverter at max capacity would be drawing iro 125AMPs so you will need to install much thicker cables than those usualy available in cars.