Given a compact, connected,
k-dimensional, oriented Lie group G or a faithful orthogonal representation T of such
a G there arises an element of the k-th framed cobordism group Ωkfr. The study of
these elements is begun, and some algebraic properties of the situation are discussed.
The remaining problem is to relate such properties of the elements in Ωkfr as order
or Adams d and e invariants to Lie theory.