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We recently introduced a class of ${\mathbb{Z}}_N$ graded discrete Lax pairsand studied the associated discrete integrable systems (lattice equations). Inthis paper we introduce the corresponding Yang-Baxter maps. Many well knownexamples belong to this scheme for $N=2$, so, for $N\geq 3$, our systems may beregarded as generalisations of these.  In particular, for each $N$ we introduce a generalisation of the map$H_{III}^B$ in the classification of scalar Yang-Baxter maps. For $N=3$ this isequivalent to the Yang-Baxter map associated with the discrete modifiedBoussinesq equation. For $N\geq 5$ (and odd) we introduce a new family ofYang-Baxter maps, which have no lower dimensional analogue. We also presentmulti-component versions of the Yang-Baxter maps $F_{IV}$ and $F_V$ (given inthe ABS classification).

${\mathbb{Z}}_N$ graded discrete Lax pairs and Yang-Baxter maps