  Let $\mathfrak{g}$ be a finite-dimensional semisimple complex Lie algebra and
$\theta$ an involutive automorphism of $\mathfrak{g}$. According to G. Letzter,
S. Kolb and M. Balagovi\'c the fixed-point subalgebra $\mathfrak{k} =
\mathfrak{g}^\theta$ has a quantum counterpart $B$, a coideal subalgebra of the
Drinfeld-Jimbo quantum group $U_q(\mathfrak{g})$ possessing a universal
K-matrix $\mathcal{K}$. The objects $\theta$, $\mathfrak{k}$, $B$ and
$\mathcal{K}$ can all be described in terms of Satake diagrams. In the present
work we extend this construction to generalized Satake diagrams, combinatorial
data first considered by A. Heck. A generalized Satake diagram naturally
defines a semisimple automorphism $\theta$ of $\mathfrak{g}$ restricting to the
standard Cartan subalgebra $\mathfrak{h}$ as an involution. It also defines a
subalgebra $\mathfrak{k}\subset \mathfrak{g}$ satisfying $\mathfrak{k} \cap
\mathfrak{h} = \mathfrak{h}^\theta$, but not necessarily a fixed-point
subalgebra. The subalgebra $\mathfrak{k}$ can be quantized to a coideal
subalgebra of $U_q(\mathfrak{g})$ endowed with a universal K-matrix in the
sense of Kolb and Balagovi\'c. We conjecture that all such coideal subalgebras
of $U_q(\mathfrak{g})$ arise from generalized Satake diagrams in this way.
