Fixed point groups of involutions of type O(q, k ) over a field of characteristic two

For G=O⁡(q,k), the orthogonal group over a field k of characteristic 2 with respect to a quadratic form q, we discuss the G-conjugacy classes of fixed points of involutions. When the quadratic space is either totally singular or nonsingular, a full classification of the isomorphism classes is given. We also give some implications of these results for a general quadratic space over a field of characteristic 2.