Title: On generalized Dold manifolds,
Abstract: Let $X$ be a smooth manifold with a (smooth) involution $\sigma:X\to X$ such
that $Fix(\sigma)\ne \emptyset$. We call the space $P(m,X):=\mathbb{S}^m\times
X/\!\sim$ where $(v,x)\sim (-v,\sigma(x))$ a generalized Dold manifold. When
$X$ is an almost complex manifold and the differential $T\sigma: TX\to TX$ is
conjugate complex linear on each fibre, we obtain a formula for the
Stiefel-Whitney polynomial of $P(m,X)$ when $H^1(X;\mathbb{Z}_2)=0$. We obtain
results on stable parallelizability of $P(m,X)$ and a very general criterion
for the (non) vanishing of the unoriented cobordism class $[P(m,X)]$ in terms
of the corresponding properties for $X$. These results are applied to the case
when $X$ is a complex flag manifold.