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At the moment I tend to believe that the Schubert cell decomposition of $BSO(n)$ is not regular (the attaching map can be 2:1 on the codimenison 2 "faces" already, I guess).
Thanks for your warning! Another popular-style reference is books.google.com/books?id=mXWr00HurmMC&pg=PA97 that I have read myself! (If I did not find the story boring then and remembered it, I would not get trapped now:))
