FUSE observations of interstellar and intergalactic absorption toward the X-ray-bright BL Lacertae object Markarian 421

High-quality Far Ultraviolet Spectroscopic Explorer (FUSE) observations at 20 km s(-1) resolution of interstellar and intergalactic absorption from 910 to 1187 Angstrom are presented for the X-ray-bright BL Lac object Mrk 421. These observations are supplemented with FUSE data for the distant halo stars BD + 38degrees2182 and HD 93521 near the Mrk 421 line of sight, in order to obtain information about the distance to absorbing structures in the Milky Way toward Mrk 421. The FUSE ISM observations provide measures of absorption by O VI and many other species commonly found in warm neutral and warm ionized gas, including H I, C II, C III, O I, N I, N II, Fe II, and Fe III. In this study we consider the O VI absorption between -140 and 165 km s(-1) and its relationship to the lower ionization absorption and strong absorption produced by O VII and O VIII at X-ray wavelengths. The O vi absorption extending from - 140 to 60 km s(-1) is associated with strong low-ionization gas absorption and originates in the Galactic thick disk/halo. This O VI appears to be produced by a combination of processes, including conductive interfaces between warm and hot gas and possibly cooling Galactic fountain gas and hot halo gas bubbles. The O vi absorption extending from 60 to 165 km s(-1) has unusual ionization properties in that there is very little associated low-ionization absorption, with the exception of C III. This absorption is not observed toward the two halo stars, implying that it occurs in gas more distant than 3.5 kpc from the Galactic disk. Over the 60 - 165 km s(-1) velocity range, O VI and C III absorption have the same kinematic behavior. The ratio N( O VI)/N(C III) = 10 +/- 3 over the 60 - 120 km s(-1) velocity range. Given the association of O VI with C III, it is unlikely that the high-velocity O vi coexists with the hotter gas responsible for the O VII and O VIII absorption. The O vi positive velocity absorption wing might be tracing cooler gas entrained in a hot Galactic fountain outflow. The O VII and O VIII absorption observed by Chandra and XMM-Newton may trace the hot gas in a highly extended ( similar to 100 kpc) Galactic corona or hot gas in the Local Group. The low resolution of the current X-ray observations (similar to 750 - 900 km s(-1)) and the kinematical complexity of the O VI absorption along typical lines of sight through the Milky Way halo make it difficult to clearly associate the O vi absorption with that produced by O VII and O VIII. A search for metal lines associated with the Lyalpha absorber at z = 0.01, which is situated in a galactic void, was unsuccessful.