Mounting pull-up/exercise beam in corner above window
No, there's no problem doing so. In fact, you probably have the best substructure there. You'll find a 2x6 or larger header either directly above the window or below the top wall plate. You should also find "cripple" or "pin" studs on standard centers over or under the header. 

Be aware that some header designs leave a 1/2" or larger insulated gap between the framing and the drywall if the load-bearing members are sandwiched together and installed at the outside of the wall thickness. You could potentially cause significant drywall damage by pulling your lumber tight with bolts. Press firmly on the drywall where you plan on bolting to feel for flex, then proceed slowly when tightening, keeping an eye out for movement.