such that $Pu=v$. Therefore, each $O_i$ is an orbit of $Z_2^n$ under the action of $W$. A Cayley graph $Cay(Z_2^n,S)$ is called an *orbit Cayley graph* if $S$ is the union of some $O_i$. In this paper, we present a simpler criterion for a Cayley graph to be strongly regular. By using this criterion and some combination identities, we construct eight infinite families of strongly regular graphs among the orbit Cayley graphs over $Z_2^n$, in which six families are new as we know. By the way, we formulate the spectra of orbit Cayley graphs over $Z_2^n$. At last, we propose two research problems.

Orbit Cayley graphs over $Z_2^n$
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We start with the connectivities of orbit Cayley graphs. Since $Cay(Z_2^n,O_0)$ is the union of $2^n$ copies of loops and $Cay(Z_2^n,O_n)$ is the union of $2^{n-1}$ copies of $K_2$, we exclude them when we consider the connectivity of an orbit Cayley graph.

\[lem-z-1\] For $i\not\in\{0,n\}$, the set $O_i$ is a generating set of $Z_2^n$ if and only if $i$ is odd.

If $i$ is even, then $O_i$ generates a subgroup in which each element $v$ satisfies that $|v|$ is even. The necessity follows. Now suppose that $i$ is an odd. If 