Is where an oracle B in EXP that $P^B$ $ \ne$ $NP^B$? According to Baker, Gill, Solovey where is an oracle A in EXP, so $P^A$ = $NP^A$. But is there an oracle B in EXP, what $P^B$ $\ne$ $NP^B$?
Yes, the Baker-Gill-Solovay B oracle is itself in EXP.