In this paper, considering the kth shape loop space Ω ˇ p k -X, x-, for an HPol∗-expansion p : -X, x- → --Xλ, xλ-, [pλλ], Λ- of a pointed topological space -X, x-, first we show that Ω ˇ p k-X, x- is an H-group for every topological space -X, x-. Then we prove that Ω ˇ c k : T op∗ −→ T op∗ is a functor, for all k ∈ N0, where c is the Čech HPol∗-expansion of spaces. Moreover, with some assumptions, we show that if X is πk-shape injective, then X is k-homotopically Hausdorff. Finally, we show that the long exact sequence of shape groups -coarse shape groups- of a pointed pair of certain spaces, is also exact as topological groups.

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