What was found
IN CRUISE AT FL410, WE GOT A "AUTO PRES FAIL" EICAS MESSAGE. IMMEDIATELY STARTED A DECENT TO A LOWER ALTITUDE AND RAN CHECKLIST BUT THE CABIN PRESSURE WOULD NOT RESPOND TO MANUAL INPUTS. THE CABIN WAS CLIMBING AT ABOUT 4400FPM AT THIS POINT SO WE WENT ON O2 & DID AN EMERGENCY DECENT TO 10,000'. THE CABIN WAS FLUCTUATING AT THIS POINT TO CLIMBING AND/OR DENDING AT RATES UP TO 4000 FPM SO WE ASKED FOR A PRIORITY APPROACH INTO TUL. DURING THE APPROACH THE CABIN ALT AND RATE INDICATORS WOULD REVERT TO DASHES GIVING US NO INDICATIONS BUT WE COULD FEEL THE PRESSURE SWINGS IN OUR EARS. UPON LANDING, THE CABIN ALTITUDE CAME BACK AND INDICATED MINUS 9200 FEET. WE TURNED ON THE APU TO TRY TO EQUALIZE THE PRESSURE WITH THAT BUT THAT DIDNT HELP. WE TURNED OFF THE APU AND TAXIED IN WITH THE ENGINES RUNNING BUT THE BLEEDS SELECTED OFF. THE CABIN BEGAN TO RISE VERY SLOWLY SO WE SAT ON THE RAMP FOR ABOUT 10 MINUTES UNTIL THE CABIN GOT TO FIELD ELEVATION. WE THEN SELECTED EMER DEPRESS AND SHUT DOWN THE ENGINES. WE HAD THE FBO VERIFY THE DOOR AREA WAS CLEAR AND OPENED THE CABIN DOOR WITHOUT ISSUE. CORRECTIVE ACTION: TECHS SUMBITTED MDC DOWNLOADS TO MCC IAW AMM 45-45-01. MCC REQUEST TECHS REMOVED AND REPLACED BOTH THE OUTFLOW VALVE AND IASC #2. TECHS R & R THE OUTFLOW VALVE WITH A SUPPLIED REPAIRED UNIT IAW AMM 21-31-05. NO DEFECTS NOTED. TECHS REMOVED AND REPLACED THE IASC #2 WITH A SUPPLIED REPAIRED UNIT IAW AMM 21-31-01. ALL OPS CHECKS ARE GOOD NO DEFECTS.