how much research has been done into cross-cultural variation of cognitive biases?

Some research has been done, but not that much. The resources required for such studies is generally pretty intensive. But most of the literature suggests that cognitive biases don't change that much between cultures. For example, the literature on the Monty Hall problem shows that the the answer rates look nearly identical in all tested cultures (which include the US, Britain, China and Brazil among others). This is discussed with further references in Jason Rosenhouse's book "The Monty Hall Problem." I'm under the impression that there's similar literature for confirmation bias, but I don't have any citations off hand.