[abridged] The metallicities of AGN are usually well above solar in their NLR, often reaching up to several times solar in their broad-line regions. Low-metallicity AGN are rare objects which have so far always been associated with low-mass galaxies hosting low-mass BHs (M_BH<10^6Msun). In this paper we present IFS data of the low-redshift QSO HE 2158-0107 for which we find strong evidence for sub-solar NLR metallicities associated with a massive BH (M_BH~3x10^8Msun). The QSO is surrounded by a large extended emission-line region reaching out to 30kpc from the QSO in a tail-like geometry. We present optical and near-IR images and investigate the properties of the host galaxy. The SED of the host is rather blue, indicative of a significant young age stellar population formed within the last 1Gyr. A 3sigma upper limit of L_bulge<4.5x10^10Lsun for the H band luminosity and a corresponding stellar mass upper limit of M_bulge<3.4x10^10Msun show that the host is offset from the local BH-bulge relations. This is independently supported by the kinematics of the gas. Although the stellar mass of the host galaxy is lower than expected, it cannot explain the exceptionally low metallicity of the gas. We suggest that the extended emission-line region and the galaxy growth are caused by the infall of nearly pristine gas from the environment of the QSO host. Minor mergers of dwarf galaxies or the theoretically predicted smooth accretion of cold gas are both potential drivers behind that process. Since the metallicity of the gas in the NLR is much lower than expected, we suspect that the external gas has already reached the galaxy centre and may even contribute to the current feeding of the BH. HE 2158-0107 appears to represent a particular phase of substantial BH and galaxy growth that can be observationally linked with the accretion of external material from its environment.
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