Benton Fraser? 
Both Dudley Do-Right and Sgt Preston were created by Americans. 
Not Oblomov?
Sweden: Pippi Longstocking (aka Pippilotta Viktualia Rullgardina Krusmynta Efraimsdotter Långstrump)
You can’t ascribe it to a modern state, so for Arabia as a region, I propose Sinbad. (according to the story, he was from Basra, so maybe modern Irak fits best.)
No, it’s definitely King David. He’s the warrior-poet, the fighter and the lover, the prankster and giant-slayer and BFF. Moses may be the greater religious figure, but David is the cultural icon.
I concur. He’s really the more interesting and juicier character in a folk sense.
Russia: Baba Yaga
George MacDonald Fraser once wrote that “Hollywood did more to promote the British Empire than the British Army.” 
Oooookay…
OK, I’ve learned two things in this thread. First, I’d always assumed that the boy who put his thumb in the dike was of Dutch origin, but it turns out he was the product of an American. And second, I’d assumed that William Tell was a well-established historical figure (whose deeds might have been exaggerated, but then, so were George Washington’s), but it turns out that he’s a legend whose historicity is disputed.
USA - Norman Bates
Germany - Baron Munchausen
Sweden - Death (from The Seventh Seal)
Denmark - Reptilicus
Then let’s just go with Arnold Winkleried for Switzerland. Good strong Doper name, too.
Or maybe Chichikov? 
Czech Republic: The Good Soldier Švejk
Sorry, terentii: Chichikov was unknown to me until now.
ETA: Then why not Prince Lev Nikolayevich Myshkin, the Idiot? (at least I knew him).
Väinämöinen
How about Merlin?
And for the US: The Little Tramp
(OK, so Chaplin was British, but the Tramp character was created in the US.)
j
ETA: and for Scotland, Nessie!
Wouldn’t some Brothers Grimm characters like Sleeping Beauty, Little Red Riding Hood, etc… be appropriately homegrown for Germany?
Crocodile Dundee?
For some of those, at least, it’s hard to track down the origin. About Sleeping Beauty, Wikipedia says “The version that was later collected and printed by the Brothers Grimm was an orally transmitted version of the literary tale published by Perrault” (who was French).
I don’t know that there are any fairy tale characters that I associate specifically with Germany, as opposed to just “Medieval European Fairty-Tale Land.”
Hänsel und Gretel?