Actions on Dold manifolds
P
(
m
,
2
k
)
P(m,{2^k})
are constructed to determine the ideals
I
∗
,
k
2
k
\mathcal {I}_{ \ast ,k}^{{2^k}}
of cobordism classes in
N
∗
{\mathcal {N}_ \ast }
containing a representative admitting a
(
Z
2
)
k
{({{\mathbf {Z}}_2})^k}
-action with fixed point set of codimension
2
k
{2^k}
.