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16 pags., 11 figs., 5 tabs. ; Context. The [C II] 158 μm fine-structure line is one of the dominant coolants of the neutral interstellar medium. It is hence one of the brightest far-infrared (FIR) emission lines and can be observed not only in star-forming regions throughout the Galaxy, but also in the diffuse interstellar medium and in distant galaxies. [C II] line emission has been suggested to be a powerful tracer of star formation. Aims. We aim to understand the origin of [C II] emission and its relation to other tracers of interstellar gas and dust. This includes a study of the heating efficiency of interstellar gas as traced by the [C II] line to test models of gas heating. Methods. We made use of a one-square-degree map of velocity-resolved [C II] line emission toward the Orion Nebula complex, including M 43 and NGC 1977. We employed Herschel FIR photometric images to determine dust properties. Moreover, we compared with Hα emission from the ionized gas, Spitzer mid-infrared photometry to trace hot dust and large polycyclic aromatic hydrocarbons (PAHs), and velocity-resolved IRAM 30m CO(2-1) observations of the molecular gas. Results. The [C II] intensity is tightly correlated with PAH emission in the IRAC 8 μm band and FIR emission from warm dust. However, the [C II] intensity depends less than linearly on the 8 μm and FIR intensity, while 8 μm and FIR intensities are approximately linearly correlated. The correlation between [C II] and CO(2-1) does not show a clear trend and is affected by the detailed geometry of the region. We find particularly low [C II]-over-FIR intensity ratios toward large columns of (warm and cold) dust, which suggest the interpretation of the "[C II] deficit"in terms of a "FIR excess". Conclusions. In terms of the [C II] deficit, we find clear evidence in our data for the importance of [O I] 63 μm emission in the photodissociation regions (PDRs) associated with the Huygens region. A smaller contribution is made by a decreased heating efficiency in regions of high UV irradiation. FIR emission from deeply embedded protostars leads to palpably deficient [C II]/FIR intensity ratios. The [C II] directly associated with the M 42, M 43, and NGC 1977 regions underestimates the star formation rate derived from extragalactic scaling relations. We ascribe this to the importance of [C II] emission from low surface brightness PDR surfaces of molecular clouds which are not included in our survey. Future studies of more active regions of massive star formation will be instrumental in validating the general applicability of these conclusions. ; This work is based on observations made with the NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is jointly operated by the Universities Space Research Association, Inc. (USRA), under NASA contract NNA17BF53C, and the Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 0901 to the University of Stuttgart. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 851435). JRG thanks the Spanish MCIU for funding support under grants AYA2017-85111-P and PID2019-106110GB-I00. Research on the interstellar medium at Leiden Observatory is supported through a Spinoza award of the Dutch Science Organisation (NWO).