98 Impreza turbo fuel starvation

[Christopher White]

Newbie to the club, can anyone help, I have a 1998 impreza 2000 turbo wagon. The engine set up is standard, the original standard exhaust was rotten so I replaced it with a second hand 3” stainless system, it’s turbo back and as far as I’m aware has no catalyst on it. When you drive the car it’s ok for a bit but then starts cutting out , being starved of fuel, also ‘check engine’ light is coming on and off. Could it be fuel pump or is it engine management? 
Thanks 👍🏻

[Tidgy]

i dont think check engine light comes on for afr's, how do you know its a fueling issue?