The challenge of leading in different cultures is a great one. While some prefer the term global leader, this would really apply to a small number of individuals and a very small number of corporations.
Realistically, you can only develop expertise in depth for two or three cultures. All the rest are understood at a very superficial and stereotypical level. For example, one will generalize and assume that the French all drink wine or the Koreans never each hamburgers.
But there are also general cultural patterns one can take advantage of. For example, there are a set of culture values that define the East and the West. These values generally apply to most counties in the region.