Hi all! any idea about how to compute the orientation character for the classifying space of the dihedral group? Since I've not found a geometric description of BD_{2n} (n even) it's hard to guess whether the loops preserve of reverse the orientation. Are there any other ways to figure it out? My aim is to identify the orientation cover, which for other reason can be either: two copies of BD_2n, BD_2(n/2), or BZ_n. But I've no clue how to show which one is the right one