Abstract: Let (M,T) be a smooth closed manifold with a smooth involution T and F={x|T(x)=x, x∈M}the fixed point set of Ton M, the authors studied the closed mainfold (M,T) with involution Tof F=RP⁵×RP^2s, and determined the possible dimensions and equivariant cobordism classification of (M,T).

Key words: involution, fixed point set, projective space, charac teristic class, cobordism class