In this paper the author proves a conjecture of \textit{M. Kashiwara} [Adv. Stud. Pure Math. 14, 369-378 (1988; Zbl 0699.22024)] which we will explain briefly below. Let \(G_R\) be a connected real semisimple linear algebraic group, \(G_C\) its complexification, \(B\) a Borel subgroup of \(G_C\), \(X = G_C/B\) the corresponding flag manifold, \(K_R \subseteq G_R\) a maximal compact subgroup, and \(K_C \subseteq G_C\) its complexification. Let \(V\) be a Harish-Chandra module with trivial infinitesimal character, and \(\Theta_V\) its global character considered as an invariant distribution on \(G_R\). Via Beilinson-Bernstein correspondence \(V\) corresponds to the \(K_C\)-equivariant \({\mathcal D}_X\)-module \({\mathcal M} = {\mathcal D}_X \otimes_{\Gamma (X, {\mathcal D}_X)} V\) from which it can be obtained as the space of global sections \(V = \Gamma (X, {\mathcal M})\). By the Riemann-Hilbert correspondence \({\mathcal M}\) corresponds to the object \({\mathcal F} : = R \Hom_{{\mathcal D}_X} ({\mathcal O}_X, {\mathcal M}) \in D_{K_C} (X)\). Furthermore, according to the Matsuki correspondence, the categories \(D_{G_R} (X)\) and \(D_{K_C} (X)\) are equivalent, and \({\mathcal F} \in D_{K_C} (X)\) corresponds to an \({\mathcal F}^a \in D_{G_R} (X)\). Let \(\widetilde G_C : = \{(g,x) \in G_C \times X : g.x = x\}\) and \(p : \widetilde G_C \to G_C\) the projection onto the first factor. Further let \(or_{G_R}\) denote the orientation sheaf of \(G_R\) with coefficients in \(C\). Then the global character \(\Theta_V\) corresponds to a Borel-Moore homology class \(cc (\Theta_V) \in H^{BM}_{\dim G_R} (p^{-1} (G_R), or_{G_R})\) which is called the character cycle. On the other hand one has a natural map \[ \Hom ({\mathcal F}^a, {\mathcal F}^a) \to H^{BM}_{ \dim G_R} \bigl( p^{-1} (G_R), orG_R \bigr), \] and the image \(ch ({\mathcal F}^a)\) of the identity under this map is called the character cycle of \({\mathcal F}^a\). The aforementioned conjecture of Kashiwara states that both character cycles coincide, i.e., \(ch ({\mathcal F}^a) = ch (\Theta_V)\). He gave a proof for Harish-Chandra modules corresponding to discrete series representations and in the paper under review the author shows that it is true in general.