It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family Wa(X) of elements of the groups Ko(Z[no(WH(X))%]). We prove that every family {u>} of elements of the groups Ko(Z[iro(WH(X))a]) can be realized as the family of equivariant finiteness obstructions Wa (X) of an appropriate finitely dom?inated G-complex X, As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall's obstruction ([1], [2]).
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