A G-homotopy equivalence \(f: X\to Y\) with no G-homotopy inverse is called exotic and so X is called G-exotic homotopy Y. We remark in section 2 that the quasi-equivalences in the book by \textit{T. Petrie} and \textit{W. Iberkleid} [(*) Smooth \(S^ 1\)-manifolds, Lect. Notes Math. 557 (1978; Zbl 0345.57016), p. 21], whose classification for actions of a torus T was given by \textit{A. A. Meyerhoff} [Bull. Am. Math. Soc. 81, 474-476 (1975; Zbl 0306.57017)], give exotic G-homotopic equivalences by Alexandroff compactification. In section 3 we contradict the possibility given by \textit{W. Y. Hsiang} [Cohomology theory of topological transformation groups (1975; Zbl 0429.57011), p. 108] of the inexistence of effective exotic actions of \(T^ 2\) or \(T^ 3\) in \(CP^ n\). A G- homotopy equivalence is said to be atypical if it does not satisfy the conjecture of \textit{T. Petri} in (*), p. 20, in which case is necessarily exotic. In section 5 we show the existence of atypical G-homotopy.