Katherine Schwarzenegger Arnold Schwarzenegger jeans barneys sunglasses muscle car

We're guessing Arnold picked up the tab -- and it was probably a pretty big one!

We caught up with the Terminator star and his 21-year-old daughter, Katherine, as they exited Barneys New York in Beverly Hills after a long father-daughter bonding/shopping trip, on Sunday.

After Arnold's cheating scandal broke in May, things seem to be cooling down for the Schwarzenegger fam. The former California governor was even spotted dining out with his soon-to-be ex-wife for his birthday last month!

Find out why Arnold was spotted wearing a T-shirt that read "I Survived Maria -- 1977-2010" on Monday, after the jump ...