  We define and construct mixed Hodge structures on real schematic homotopy
types of complex quasi-projective varieties, giving mixed Hodge structures on
their homotopy groups and pro-algebraic fundamental groups. We also show that
these split on tensoring with the ring R[x] equipped with the Hodge filtration
given by powers of (x-i), giving new results even for simply connected
varieties. The mixed Hodge structures can thus be recovered from the Gysin
spectral sequence of cohomology groups of local systems, together with the
monodromy action at the Archimedean place. As the basepoint varies, these
structures all become real variations of mixed Hodge structure.
