Finite Z / 2 Z {\mathbb Z}/2{\mathbb Z} -CW complexes which are not homotopically stratified by orbit type

For k≥2k \geq 2, we construct finite Z/2Z{\mathbb Z}/2{\mathbb Z}-CW complexes with one Z/2Z{\mathbb Z}/2{\mathbb Z}-cell in dimensions 00, 11 and k+1k+1. Using a theorem of Bruce Hughes, we show that these complexes are not homotopically stratified by orbit type in the sense of Quinn.