Global secondary index geo-partitioned data

An e-commerce catalog is geo-partitioned: each product record is owned by the seller's home region and writes go there. But buyers need fast global query/filter across ALL products regardless of owning region, 'show electronics under $50 shipping to Germany', sorted, paginated, p95 < 150ms from any region. Building a synchronous global index on every write would couple write latency to all regions and create a write hotspot. Design a globally-queryable secondary index over data whose source-of-truth is partitioned by region. Address index freshness vs query latency, how a buyer query is fanned out or served, and what consistency a buyer can expect between the index result and the live product record (price/stock).