An old professor of mine used to talk about "the Pizza Effect"--Italian immigrants bring Italian cooking to the States, then pizza is invented under that influence, and the Italians in Italy accept it as their own.
I have been working on translating an article about the popularity of The Book of Changes outside of Asia. The author seems surprised that foreigners could understand something that "even Chinese don't," but then goes on to talk about all the Chinese things that she's found to have been adopted abroad--feng shui, the Chinese horoscope, Lao Tzu.... She tosses around words like "mysticism," too (which these things wouldn't be in their original context). It struck me how even the Chinese author has dropped these things into this "Western" framework. Is this the Pizza Effect?
Marxy over at Neomarxisme mentions the "self-Orientalization" that goes on when Japanese perpetuate "Fujiyama Geisha" type images themselves. That doesn't stop the Japanese from getting upset over, say Memoirs of a Geisha--Marxy concludes that "the big difference [is] that the modern Japanese users of these symbols get them 'right' while Americans are often sloppy, uninformed, and implicitly racist."
Perhaps something like The Book of Changes (or Italian cooking) belongs to world culture, but the Chinese (and Italians) may reserve the right to be the curators.