We keep all the notation of Section 16 and we assume again that B .. ≅ E(B ..), so that A ..,  and Â’ still coincide with their Higman envelopes (cf. Corollary 14.21 and 15.7.1). In this section we analyze a particular kind of local tracing triples on Â, A .. and OG’ (cf. 16.4) which occurs without exception in the Hecke DG-interior algebras associated with the basic Rickard equivalences between blocks introduced in Section 19 below. Precisely, we say that a local tracing triple (P ŷ \(\left( {{P_{\hat \gamma }},P_{\gamma ..}^{..},{{P'}_{\gamma '}}} \right)\) on Â, A .. and OG’ is basic if   is a split DP-module (cf. 10.12 and 11.2) and A ŷ .. ,is a Ker(σ)-basic DP ..-interior algebra (cf. 13.2), where σ: P .. → P is the group homomorphism determined by π in this case, it is clear that any local tracing triple on Â, A .. and OG’ contained in (P ŷ \(P_{{y^{..}}}^{..},P_{{y^,}}^,\)) is basic too (cf. 14.3.1 and 16.12.1). Moreover, since (OG’) y’, has a P’ × P’-stable O-basis by left and right multiplication, the basic condition on A ŷ .. is inherited by the tensor product \(\left( {A_{{y^{..}}}^{..}} \right.{ \otimes _\vartheta }\operatorname{Re} {s_{{\sigma ^,}}}\left( {(\vartheta {G^,}} \right.){y^,}\left. ) \right)\), where σ’: P .. → P’ is the group homomorphism determined by π’, so that, by Lemma 13.4, the induced DP-interior algebra Indσ \(\left( {A_{{y^{..}}}^{..}} \right.{ \otimes _\vartheta }\operatorname{Re} {s_{{\sigma ^,}}}\left( {(\vartheta {G^,}} \right.){y^,}\left. ) \right)\) is basic and then, by the existence of the structural DP-interior algebra exoembedding \(\tilde h{\tilde y^{{y^{..}},{y^,}}}\)(cf. 16.4.1),  ŷ is a basic DP-interior algebra too: before going further, let us collect some elementary facts on basic DP-interior algebras which are split DP-modules.