This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space
R
P
j
\mathbb {RP}^j
with its normal bundle nonbounding and a Dold manifold
P
(
h
,
i
)
P(h,i)
with
h
>
0
h>0
and
i
>
0
i>0
. For odd
h
h
, the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of
P
(
h
,
i
)
P(h,i)
may not be best possible; for even
h
h
, the problem may be reduced to the problem for even projective spaces.