AN A320 CREW RPTS THE ACFT FLYING THE VOR DME2 RWY 12 AT CUN APCH NAV WITH A SIGNIFICANT OFFSET TO THE R.

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WE WERE CLRED BY APCH TO FLY THE VOR DME 2 RWY 12 APCH AND SINCE THE APCH WAS LINE SELECTABLE; WE BRIEFED AND FLEW IT AS AN APCH NAV APCH. WE HAD BEEN LEFT HIGH BY APCH AND HAD TO DEV AROUND WX JOINING THE FINAL; SO THE LAST COUPLE OF MINUTES WERE RUSHED JOINING THE APCH AND ENGAGING THE APCH MODE; HOWEVER; THE AUTOPLT CAPTURED THE GLIDESLOPE CORRECTLY FROM THE INTERCEPT ALT. PRIOR TO BEGINNING THE APCH; WE HAD INTERCEPTED THE CUN 302 RADIAL INBOUND (THE FINAL APCH COURSE) IN NAV. I HAD RAW DATA DISPLAYED WITH THE RADIAL HARD TUNED. IN NAV; THE ACFT OVERSHOT THE RADIAL TO THE R AND STAYED THERE FROM ABOUT 17 MILES OUT WHERE WE INTERCEPTED IN NAV ALL THE WAY UNTIL I DISCONNECTED THE AUTOPLT TO LINE UP FOR LNDG (ABOUT A 2 MILE FINAL). THE RAW DATA CONSISTENTLY DISPLAYED THE ACFT R OF TRACK UP TO A FULL DOT TOWARD THE END OF THE APCH. WE COULD SEE THE RWY FROM ABOUT 8 MILES OUT SO I LET THE AUTOPLT CONTINUE TO FLY THE AIRPLANE TO SEE IF IT WOULD CORRECT. IT NEVER DID. AGAIN; THE GLIDESLOPE TRACK WAS NEARLY RIGHT ON THE PAPI; BUT THE LATERAL TRACK LEFT US FAR ENOUGH TO THE R OF THE RADIAL THAT I BELIEVE THIS WOULD BE AN ISSUE IF THE APCH HAD TO BE FLOWN FOR REAL DOWN TO THE MDA OF 401 FT AGL. I DON'T THINK THIS APCH WOULD HAVE LEFT THE ACFT IN A POSITION TO COMPLETE A NORMAL TRANSITION TO VISUAL AND LAND. THE ACFT DOES NOT HAVE GPS UPDATING BUT THE DME/DME UPDATING WAS WORKING AND WE HAD THE REQUIRED RNP THROUGHOUT THE APCH.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE CAPT STATES THAT HE HAS NOT HAD THIS PROB OCCUR PREVIOUSLY IN 1200 HOURS OF FLYING THE A320. HE ALSO STATES HE USED APCH NAV ON ARR BACK IN THE US AND IT FUNCTIONED NORMALLY.