The most obvious example to me was Kevin Costner as Robin Hood.
“The most obvious example to me was Kevin Costner as Robin Hood.”
Or as anybody for that matter.
I don't universally mind American actors playing roles based on foreigners. British and Australian actors make a fine living playing Americans. But of course, they're highly trained in their craft, including the mastery of every dialect of the English spoken word, and generally speaking pull it off with most of the American audience unaware that the character playing Al Capone with a flawless Brooklyn, NY accent was born and raised in Liverpool (Stephen Graham in Boardwalk Empire).
The problem is when Hollywood decides to cast one of their can't chew gum and walk at the same time "stars". Some can pull it off, for example Edward Norton did a fine job playing an Austrian Jewish magician in The Illusionist. But most American major actors get by more on their looks than any talent or training.