  Univariate L-moments are expressed as projections of the quantile function
onto an orthogonal basis of polynomials in $L_2([0;1],\mathbb{R})$. We present
multivariate versions of L-moments expressed as collections of orthogonal
projections of a multivariate quantile function on a basis of multivariate
polynomials in $L_2([0;1]^d,\mathbb{R})$. We propose to consider quantile
functions defined as transport from the uniform distribution on $[0;1]^d$ onto
the distribution of interest. In particular, we present the quantiles defined
by the transport of Rosenblatt and the optimal transport and the properties of
the subsequent L-moments.
