  We report ultraviolet spectra of Galactic high-velocity clouds (HVCs) in
Complex C, taken by the Cosmic Origins Spectrograph (COS) on the Hubble Space
Telescope (HST), together with new 21-cm spectra from the Green Bank Telescope.
The wide spectral coverage and higher S/N, compared to previous HST spectra,
provide better velocity definition of the HVC absorption, additional ionization
species, and improved abundances in this halo gas. Complex C has a metallicity
of 0.1-0.3 solar and a wide range of ions, suggesting dynamical and thermal
interactions with hot gas in the Galactic halo. Spectra in the COS
medium-resolution G130M (1133-1468 A) and G160M (1383-1796 A) gratings detect
ultraviolet absorption lines from 8 elements in low ionization stages (O I, N
I, C II, S II, Si II, Al II, Fe II, P II) and 3 elements in intermediate and
high-ionization states (Si III, Si IV, C IV, N V). Our four AGN sight lines
toward Mrk 817, Mrk 290, Mrk 876, and PG1259+593 have high-velocity H I and O
VI column densities, log N_HI = 19.39-20.05 and log N_OVI = 13.58-14.10, with
substantial amounts of kinematically associated photoionized gas. The high-ion
abundance ratios are consistent with cooling interfaces between photoionized
gas and collisionally ionized gas: N(C IV)/N(O VI) = 0.3-0.5, N(Si IV)/N(O VI)
= 0.05-0.11, N(N V)/N(O VI) = 0.07-0.13, and N(Si IV)/N(Si III) = 0.2.
