Batch Normalization For Federated Learning
One approach would be to simply average everything, as proposed in the FedAvg preprint.
Some very recent preprints suggest only relaying the learned parameters back to the central server and keeping local batch normalization (BN) statistics separate, as proposed by the SiloBN preprint.
The authors of this paper claim that:

Keeping BN statistics local permits the federated training of a model robust to the heterogeneity of the different centers, as the local statistics ensure that the intermediate activations are centered to a similar value across centers.

To paraphrase them; they distinguish BN statistics as encodings for local domain information whereas the learned parameters are to be domain-invariant. I believe their aggregation method for the relayed information is simply averaging.
Here's their first figure for reference: