This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω t } t∈[0,1] on a locally compact Hausdorff groupoid G induces an isomorphism of the Ktheory groups of the reduced twisted groupoid C * -algebras:). Generalizing work of Echterhoff et al. from [6], we show that if G = G ⋉ X is a transformation group such that G satisfies the Baum-Connes conjecture with coefficients, a homotopy ω = {ω t } t∈[0,1] of 2-cocycles on G ⋉ X gives rise to an isomorphism K * (C * r (G ⋉ X, ω 0 )) ∼ = K * (C * r (G ⋉ X, ω 1 )).