It doesn’t have to be famous, just a work that you connect with that you feel represents your country in some way.
I’m from America so of course our literary classics are pretty widely known in the western world, so I’m going to recommend something a bit more niche: There There by Tommy Orange. It shines light on many different aspects of the Native American experience, specifically in Oakland, California. It covers addiction, poverty, culture, and heritage in a way that I (not Native myself) found moving.
The usual answer for Sweden is “The Emigrants” (Utvandrarna) by Vilhelm Moberg. However, and I don’t think this is obvious to foreign readers, the author John Ajvide Lindqvist really writes about Sweden. He’s most famous for the book “Let the right one in” about a vampire kid, but the story is actually about growing up as a young boy in Sweden. The horror aspect is part of the genre, but all his books manage to mix a description of swedish society with a supernatural horror element.
Maybe the obvious answer, but East of Eden. It’s a genuine masterpiece.