Chow ring of B O2(2n) in characteristic 2

For n >= 1, let SO(2n) be the special orthogonal group given by the standard split nondegenerate 2n-dimensional quadratic form over a field. The Chow ring CH(B SO(2n)) of its classifying space has been computed for the field of complex numbers in 2000 by R. Field. Arbitrary fields of characteristic not equal 2 have been treated, using a different method, in 2006 by L. A. Molina Rojas and A. Vistoli. Using specialization from characteristic 0, we extend their computation to characteristic 2.