Fotos..........

Yes, we need pics to help you out. Sounds like the pot size is way too small, but that's only a guess without pics.

If the plant is fully hardened-off, I can't think of a reason it should not be in full sun. Perhaps under-watering and too small a pot is the issue? Peppers certainly don't like "wet feet", but will require regular watering when in full sun. It should not get *too* droopy/wilted before being watered ideally. When it looks thirsty, it's good to give it a good soak, assuming a well-draining medium, until water comes out of the draining holes. Watering only a little at a time tends to keep the top moist, but the bottom of the pot can dry out without us knowing.