Yeah, worrying times in Sweden now, but you won't get an AR. Sorry. The AR15 is not approved for hunting in Sweden, to get one you would need a sportshooting licence. Specifically one for dynamic shooting (essentially a run and gun sport), which are notoriously hard to get. You need to be a member of a shootingclub for 6 months and then they need to vouch for you to the Police, that you do indeed train and compete in the sport, in order for them to issue you a licence. A hunting licence would be your best bet to get a gun.
Hypothetically, if you were interrested in hunting with a high capacity magazine. The Ruger PCC would be your best bet. It takes 9mm Glock magazines and you can get 25 rounders for that.
(Obviously if SÄPO is reading any of this, the above only pertains to actually hunting, I completely disavow of the derogatory comment made regarding people of the African persuasion and distance my self from all that criminal violence entails.)