Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT

It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature.  I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.