Homotopy decompositions of looped 2-cell co-H spaces

Let p be an odd prime. For certain p-local 2-cell co-H spaces Y, we consider the homotopy decomposition of ΩY. First we give an explicit description of the stable splitting of ΩY, which refines Jamesʹ classical result on stable splittings of loop suspension. Also we show that the product decomposition of ΩY has as a factor Ω Σ f ( k ) Y for f ( k ) a linear function for k ≥ 0 .